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図書

図書
Vladimir G. Maz'ya, Tatyana O. Shaposhnikova
出版情報: Berlin : Springer, c2009  xiii, 609 p. ; 25 cm
シリーズ名: Die Grundlehren der mathematischen Wissenschaften ; v. 337
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Introduction
Description and Properties of Multipliers / Part I:
Trace Inequalities for Functions in Sobolev Spaces / 1:
Trace Inequalities for Functions in <$>w_1^m<$> and <$>W_1^m<$> / 1.1:
The Case m = 1 / 1.1.1:
The Case m ≥ 1 / 1.1.2:
Trace Inequalities for Functions in <$>w_p^m<$> and <$>W_p^m<$>, p > 1 / 1.2:
Preliminaries / 1.2.1:
The (p, m)-Capacity / 1.2.2:
Estimate for the Integral of Capacity of a Set Bounded by a Level Surface / 1.2.3:
Estimates for Constants in Trace Inequalities / 1.2.4:
Other Criteria for the Trace Inequality (1.2.29) with p > 1 / 1.2.5:
The Fefferman and Phong Sufficient Condition / 1.2.6:
Estimate for the Lq-Norm with respect to an Arbitrary Measure / 1.3:
The case 1 ≤ p < q / 1.3.1:
The case q < p ≤ n/m / 1.3.2:
Multipliers in Pairs of Sobolev Spaces / 2:
Characterization of the Space <$>M(W_1^m \to W_1^l)<$> / 2.1:
Characterization of the Space <$>M(W_p^m \to W_p^l)<$> for p > 1 / 2.3:
Another Characterization of the Space <$>M(W_p^m \to W_p^l)<$> for 0 < l < m, pm ≤ n, p > 1 / 2.3.1:
Characterization of the Space <$>M(W_p^m \to W_p^l)<$> for pm > n, p > 1 / 2.3.2:
One-Sided Estimates for Norms of Multipliers in the Case pm ≤ n / 2.3.3:
Examples of Multipliers / 2.3.4:
The Space <$>M(W_p^m\left( {\op R}_+^n \right) \to W_p^l({\op R}_+^n))<$> / 2.4:
Extension from a Half-Space / 2.4.1:
The Case p > 1 / 2.4.2:
The Case p = 1 / 2.4.3:
The Space <$>M(W_p^m \to W_p^{-k})<$> / 2.5:
The Space <$>M(W_p^m \to W_q^l)<$> / 2.6:
Certain Properties of Multipliers / 2.7:
The Space <$>M(w_p^m \to w_p^l)<$> / 2.8:
Multipliers in Spaces of Functions with Bounded Variation / 2.9:
The Spaces Mbv and MBV / 2.9.1:
Multipliers in Pairs of Potential Spaces / 3:
Trace Inequality for Bessel and Riesz Potential Spaces / 3.1:
Properties of Bessel Potential Spaces / 3.1.1:
Properties of the (p, m)-Capacity / 3.1.2:
Main Result / 3.1.3:
Description of <$>M(H_p^m \to H_p^l)<$> / 3.2:
Auxiliary Assertions / 3.2.1:
Imbedding of <$>M(H_p^m \to H_p^l)<$> into <$>M(H_p^{m-l} \to L_p)<$> / 3.2.2:
Estimates for Derivatives of a Multiplier / 3.2.3:
Multiplicative Inequality for the Strichartz Function / 3.2.4:
Auxiliary Properties of the Bessel Kernel Gl / 3.2.5:
Upper Bound for the Norm of a Multiplier / 3.2.6:
Lower Bound for the Norm of a Multiplier / 3.2.7:
Description of the Space <$>M(H_p^m \to H_p^l)<$> / 3.2.8:
Equivalent Norm in <$>M(H_p^m \to H_p^l)<$> Involving the Norm in Lmp/(m-l) / 3.2.9:
Characterization of <$>M(H_p^m \to H_p^l)<$>, m > l, Involving the Norm in L1,unif / 3.2.10:
The Space <$>M(H_p^m \to H_p^l)<$> for mp > n / 3.2.11:
One-Sided Estimates for the Norm in <$>M(H_p^m \to H_p^l)<$> / 3.3:
Lower Estimate for the Norm in <$>M(H_p^m \to H_p^l)<$> Involving Morrey Type Norms / 3.3.1:
Upper Estimate for the Norm in <$>M(H_p^m \to H_p^l)<$> Involving Marcinkiewicz Type Norms / 3.3.2:
Upper Estimates for the Norm in <$>M(H_p^m \to H_p^l)<$> Involving Norms in <$>H_{n/m}^l<$> / 3.3.3:
Upper Estimates for the Norm in <$>M(H_p^m \to H_p^l)<$> by Norms in Besov Spaces / 3.4:
Properties of the Space <$>B_{q,\infty}^{\mu}<$> / 3.4.1:
Estimates for the Norm in <$>M(H_p^m \to H_p^l)<$> by the Norm in <$>B_{q,\infty}^{\mu}<$> / 3.4.3:
Estimate for the Norm of a Multiplier in <$>MH_p^l({\op R}^1)<$> by the q-Variation / 3.4.4:
Miscellaneous Properties of Multipliers in <$>M(H_p^m \to H_p^l)<$> / 3.5:
Spectrum of Multipliers in <$>H_p^l<$> and <$>H_{p^\prime}^{-l}<$> / 3.6:
Preliminary Information / 3.6.1:
Facts from Nonlinear Potential Theory / 3.6.2:
Main Theorem / 3.6.3:
Proof of Theorem 3.6.1 / 3.6.4:
The Space <$>M(h_p^m \to h_p^l)<$> / 3.7:
Positive Homogeneous Multipliers / 3.8:
The Space <$>M(H_p^m(\partial{\cal B}_1) \to H_p^l(\partial{\cal B}_1))<$> / 3.8.1:
Other Normalizations of the Spaces <$>h_p^m<$> and <$>H_p^m<$> / 3.8.2:
Positive Homogeneous Elements of the Spaces <$>M(h_p^m \to h_p^l)<$> and <$>M(H_p^m \to H_p^l)<$> / 3.8.3:
The Space <$>M(B_p^m \to B_p^l)<$> with p > 1 / 4:
Properties of Besov Spaces / 4.1:
Survey of Known Results / 4.2.1:
Properties of the Operators <$>{\cal D}_{p,l}<$> and Dp,l / 4.2.2:
Pointwise Estimate for Bessel Potentials / 4.2.3:
Proof of Theorem 4.1.1 / 4.3:
Estimate for the Product of First Differences / 4.3.1:
Trace Inequality for <$>B_p^k<$>, p > 1 / 4.3.2:
Auxiliary Assertions Concerning <$>M(B_p^m \to B_p^l)<$> / 4.3.3:
Lower Estimates for the Norm in <$>M(B_p^m \to B_p^l)<$> / 4.3.4:
Proof of Necessity in Theorem 4.1.1 / 4.3.5:
Proof of Sufficiency in Theorem 4.1.1 / 4.3.6:
The Case mp > n / 4.3.7:
Lower and Upper Estimates for the Norm in <$>M(B_p^m \to B_p^l)<$> / 4.3.8:
Sufficient Conditions for Inclusion into <$>M(W_p^m \to W_p^l)<$> with Noninteger m and l / 4.4:
Conditions Involving the Space <$>B_{q,\infty}^{\mu}<$> / 4.4.1:
Conditions Involving the Fourier Transform / 4.4.2:
Conditions Involving the Space <$>B_{q,p}^l<$> / 4.4.3:
Conditions Involving the Space <$>H_{n/m}^l<$> / 4.5:
Composition Operator on <$>M(W_p^m \to W_p^l)<$> / 4.6:
The Space <$>M(B_1^m \to B_1^l)<$> / 5:
Trace Inequality for Functions in <$>B_1^l({\op R}^n)<$> / 5.1:
Auxiliary Facts / 5.1.1:
Properties of Functions in the Space <$>B_1^k({\op R}^n)<$> / 5.1.2:
Trace and Imbedding Properties / 5.2.1:
Auxiliary Estimates for the Poisson Operator / 5.2.2:
Descriptions of <$>M(B_1^m \to B_1^l)<$> with Integer l / 5.3:
A Norm in <$>M(B_1^m \to B_1^l)<$> / 5.3.1:
Description of <$>M(B_1^m \to B_1^l)<$> Involving <$>{\cal D}_{1,l}<$> / 5.3.2:
<$>M(B_1^m({\op R}^n) \to B_1^l({\op R}^n))<$> as the Space of Traces / 5.3.3:
Interpolation Inequality for Multipliers / 5.3.4:
Description of the Space <$>M(B_1^m \to B_1^l)<$> with Noninteger l / 5.4:
Further Results on Multipliers in Besov and Other Function Spaces / 5.5:
Peetre's Imbedding Theorem / 5.5.1:
Related Results on Multipliers in Besov and Triebel-Lizorkin Spaces / 5.5.2:
Multipliers in BMO / 5.5.3:
Maximal Algebras in Spaces of Multipliers / 6:
Pointwise Interpolation Inequalities for Derivatives / 6.1:
Inequalities Involving Derivatives of Integer Order / 6.2.1:
Inequalities Involving Derivatives of Fractional Order / 6.2.2:
Maximal Banach Algebra in <$>M(W_p^m \to W_p^l)<$> / 6.3:
Maximal Banach Algebra in <$>M(W_1^m \to W_1^l)<$> / 6.3.1:
Maximal Algebra in Spaces of Bessel Potentials / 6.4:
Pointwise Inequalities Involving the Strichartz Function / 6.4.1:
Banach Algebra <$>{\cal A}_p^{m,l}<$> / 6.4.2:
Imbeddings ofMaximal Algebras / 6.5:
Essential Norm and Compactness of Multipliers / 7:
Two-Sided Estimates for the Essential Norm. The Case m > l / 7.1:
Estimates Involving Cutoff Functions / 7.2.1:
Estimate Involving Capacity (The Case mp < n, p > 1) / 7.2.2:
Estimates Involving Capacity (The Case mp = n, p > 1) / 7.2.3:
Proof of Theorem 7.0.3 / 7.2.4:
Sharpening of the Lower Bound for the Essential Norm in the Case m > l, mp ≤ n, p > 1 / 7.2.5:
Estimates of the Essential Norm for mp > n, p > 1 and for p = 1 / 7.2.6:
One-Sided Estimates for the Essential Norm / 7.2.7:
The Space of Compact Multipliers / 7.2.8:
Two-Sided Estimates for the Essential Norm in the Case m = l / 7.3:
Estimate for the Maximum Modulus of a Multiplier in <$>W_p^l<$> by its Essential Norm / 7.3.1:
Estimates for the Essential Norm Involving Cutoff Functions (The Case lp ≤ n, p > 1) / 7.3.2:
Estimates for the Essential Norm Involving Capacity (The Case lp ≤ n, p > 1) / 7.3.3:
Two-Sided Estimates for the Essential Norm in the Cases lp > n, p > 1, and p =1 / 7.3.4:
Essential Norm in <$>\ring M W_p^l<$> / 7.3.5:
Traces and Extensions of Multipliers / 8:
Multipliers in Pairs of Weighted Sobolev Spaces in <$>{\op R}_+^n<$> / 8.1:
Characterization of <$>M(W_p^{t,\beta} \to W_p^{s,\alpha})<$> / 8.3:
Auxiliary Estimates for an Extension Operator / 8.4:
Pointwise Estimates for Tγ and ∇Tγ / 8.4.1:
Weighted Lp-Estimates for Tγ and ∇Tγ / 8.4.2:
Trace Theorem for the Space <$>M(W_p^{t,\beta} \to W_p^{s,\alpha})<$> / 8.5:
The Case l < 1 / 8.5.1:
The Case l > 1 / 8.5.2:
Proof of Theorem 8.5.1 for l > 1 / 8.5.3:
Traces of Multipliers on the Smooth Boundary of a Domain / 8.6:
<$>MW_p^l({\op R}^n)<$> as the Space of Traces of Multipliers in the Weighted Sobolev Space <$>W_{p,\beta}^k({\op R}^{n+m})<$> / 8.7:
A Property of Extension Operator / 8.7.1:
Trace and Extension Theorem for Multipliers / 8.7.3:
Extension of Multipliers from <$>{\op R}^n<$> to <$>{\op R}_+^{n+1}<$> / 8.7.4:
Application to the First Boundary Value Problem in a Half-Space / 8.7.5:
Traces of Functions in <$>MW_p^l({\op R}^{n+m})<$> on <$>{\op R}^n / 8.8:
Trace and Extension Theorem / 8.8.1:
Multipliers in the Space of Bessel Potentials as Traces of Multipliers / 8.9:
Bessel Potentials as Traces / 8.9.1:
An Auxiliary Estimate for the Extension Operator <$>{\cal T}<$> / 8.9.2:
<$>MH_p^l<$> as a Space of Traces / 8.9.3:
Sobolev Multipliers in a Domain, Multiplier Mappings and Manifolds / 9:
Multipliers in a Special Lipschitz Domain / 9.1:
Special Lipschitz Domains / 9.1.1:
Description of the Space of Multipliers / 9.1.2:
Extension of Multipliers to the Complement of a Special Lipschitz Domain / 9.2:
Multipliers in a Bounded Domain / 9.3:
Domains with Boundary in the Class C0,1 / 9.3.1:
Description of Spaces of Multipliers in a Bounded Domain with Boundary in the Class C0,1 / 9.3.2:
Essential Norm and Compact Multipliers in a Bounded Lipschitz Domain / 9.3.4:
The Space <$>ML_p^1(\Omega)<$> for an Arbitrary Bounded Domain / 9.3.5:
Change of Variables in Norms of Sobolev Spaces / 9.4:
(p, l)-Diffeomorphisms / 9.4.1:
More on (p, l)-Diffeomorphisms / 9.4.2:
A Particular (p, l)-Diffeomorphism / 9.4.3:
(p, l)-Manifolds / 9.4.4:
Mappings <$>T_p^{m,l}<$> of One Sobolev Space into Another / 9.4.5:
Implicit Function Theorems / 9.5:
The Space <$>M(\ring {W}_p^m(\Omega) \to W_p^l(\Omega))<$> / 9.6:
Auxiliary Results / 9.6.1:
Description of the Space <$>M(\ring {W}_p^m(\Omega) \to W_p^l(\Omega))<$> / 9.6.2:
Applications of Multipliers to Differential and Integral Operators / Part II:
Differential Operators in Pairs of Sobolev Spaces / 10:
The Norm of a Differential Operator: <$>W_p^h \to W_p^{h-k}<$> / 10.1:
Coefficients of Operators Mapping <$>W_p^h<$> into <$>W_p^{h-k}<$> as Multipliers / 10.1.1:
A Counterexample / 10.1.2:
Operators with Coefficients Independent of Some Variables / 10.1.3:
Differential Operators on a Domain / 10.1.4:
Essential Norm of a Differential Operator / 10.2:
Fredholm Property of the Schrödinger Operator / 10.3:
Domination of Differential Operators in <$>{\op R}^n<$> / 10.4:
Schrödinger Operator and <$>M (w_2^1 \to w_2^{-1})<$> / 11:
Characterization of <$>M(w_2^1 \to w_2^{-1})<$> and the Schrödinger Operator on <$>w_2^1<$> / 11.1:
A Compactness Criterion / 11.3:
Characterization of <$>M (W_2^1 \to W_2^{-1})<$> / 11.4:
Characterization of the Space <$>M(\ring {w}_2^1 (\Omega) \to w_2^{-1}(\Omega))<$> / 11.5:
Second-Order Differential Operators Acting from <$>w_2^1<$> to <$>w_2^{-1}<$> / 11.6:
Relativistic Schrödinger Operator and <$>M(W_2^{1/2} \to W_2^{-1/2})<$> / 12:
Corollaries of the Form Boundedness Criterion and Related Results / 12.1:
Multipliers as Solutions to Elliptic Equations / 13:
The Dirichlet Problem for the Linear Second-Order Elliptic Equation in the Space of Multipliers / 13.1:
Bounded Solutions of Linear Elliptic Equations as Multipliers / 13.2:
The Case β > 1 / 13.2.1:
The Case β = 1 / 13.2.3:
Solutions as Multipliers from <$>W_{2, w(\rho)}^1 (\Omega)<$> into <$>W_{2,1}^1 (\Omega)<$> / 13.2.4:
Solvability of Quasilinear Elliptic Equations in Spaces of Multipliers / 13.3:
Scalar Equations in Divergence Form / 13.3.1:
Systems in Divergence Form / 13.3.2:
Dirichlet Problem for Quasilinear Equations in Divergence Form / 13.3.3:
Dirichlet Problem for Quasilinear Equations in Nondivergence Form / 13.3.4:
Coercive Estimates for Solutions of Elliptic equations in Spaces of Multipliers / 13.4:
The Case of Operators in <$>{\op R}^n<$> / 13.4.1:
Boundary Value Problem in a Half-Space / 13.4.2:
On the L-Norm in the Coercive Estimate / 13.4.3:
Smoothness of Solutions to Higher Order Elliptic Semilinear Systems / 13.5:
Composition Operator in Classes of Multipliers / 13.5.1:
Improvement of Smoothness of Solutions to Elliptic Semilinear Systems / 13.5.2:
Regularity of the Boundary in Lp-Theory of Elliptic Boundary Value Problems / 14:
Description of Results / 14.1:
Change of Variables in Differential Operators / 14.2:
Fredholm Property of the Elliptic Boundary Value Problem / 14.3:
Boundaries in the Classes <$>M_p^{l-1/p}<$>, <$>W_p^{l-1/p}<$>, and <$>M_p^{l-1/p}(\delta)<$> / 14.3.1:
A Priori Lp-Estimate for Solutions and Other Properties of the Elliptic Boundary Value Problem / 14.3.2:
Some Properties of the Operator <$>{\cal T}<$> / 14.4:
Properties of the Mappings λ and / 14.4.2:
Invariance of the Space <$>W_p^l \cap \ring {W}_p^h<$> Under a Change of Variables / 14.4.3:
The Space <$>W_p^{-k}<$> for a Special Lipschitz Domain / 14.4.4:
Auxiliary Assertions on Differential Operators in Divergence Form / 14.4.5:
Solvability of the Dirichlet Problem in <$>W_p^l(\Omega)<$> / 14.5:
Generalized Formulation of the Dirichlet Problem / 14.5.1:
A Priori Estimate for Solutions of the Generalized Dirichlet Problem / 14.5.2:
Solvability of the Generalized Dirichlet Problem / 14.5.3:
The Dirichlet Problem Formulated in Terms of Traces / 14.5.4:
Necessity ofAssumptions on the Domain / 14.6:
A Domain Whose Boundary is in <$>M_2^{3/2} \cap C^1<$> but does not Belong to <$>M_2^{3/2} (\delta)<$> / 14.6.1:
Necessary Conditions for Solvability of the Dirichlet Problem / 14.6.2:
Boundaries of the Class <$>M_p^{l-1/p} (\delta)<$> / 14.6.3:
Local Characterization of <$>M_p^{l-1/p} (\delta)<$> / 14.7:
Estimates for a Cutoff Function / 14.7.1:
Description of <$>M_p^{l-1/p} (\delta)<$> Involving a Cutoff Function / 14.7.2:
Estimate for s1 / 14.7.3:
Estimate for s2 / 14.7.4:
Estimate for s3 / 14.7.5:
Multipliers in the Classical Layer Potential Theory for Lipschitz Domains / 15:
Solvability of Boundary Value Problems in Weighted Sobolev Spaces / 15.1:
(p, k, α)-Diffeomorphisms / 15.2.1:
Weak Solvability of the Dirichlet Problem / 15.2.2:
Continuity Properties of Boundary Integral Operators / 15.2.3:
Proof of Theorems 15.1.1 and 15.1.2 / 15.4:
Proof of Theorem 15.1.1 / 15.4.1:
Proof of Theorem 15.1.2 / 15.4.2:
Properties of Surfaces in the Class <$>M_p^{\ell}(\delta)<$> / 15.5:
Sharpness of Conditions Imposed on &partial;Ω / 15.6:
Necessity of the Inclusion <$>\partial \Omega \in W_p^{\ell}<$> in Theorem 15.2.1 / 15.6.1:
Sharpness of the Condition <$>\partial \Omega \in B_{\infty,p}^{\ell}<$> / 15.6.2:
Sharpness of the Condition <$>\partial \Omega \in M_p^{\ell} (\delta)<$> in Theorem 15.2.1 / 15.6.3:
Sharpness of the Condition <$>\partial \Omega \in M_p^{\ell}(\delta)<$> in Theorem 15.1.1 / 15.6.4:
Extension to Boundary Integral Equations of Elasticity / 15.7:
Applications of Multipliers to the Theory of Integral Operators / 16:
Convolution Operator in Weighted L2-Spaces / 16.1:
Calculus of Singular Integral Operators with Symbols in Spaces of Multipliers / 16.2:
Continuity in Sobolev Spaces of Singular Integral Operators with Symbols Depending on x / 16.3:
Function Spaces / 16.3.1:
Description of the Space M(Hm,μ → Hl,μ) / 16.3.2:
Corollaries / 16.3.3:
References
List of Symbols
Author and Subject Index
Introduction
Description and Properties of Multipliers / Part I:
Trace Inequalities for Functions in Sobolev Spaces / 1:
2.

図書

図書
K. Clancey, I. Goherg
出版情報: Basel ; Boston : Birkhäuser Verlag, 1981  x, 234 p. ; 25 cm
シリーズ名: Operator theory, advances and applications ; v. 3
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3.

図書

図書
K. Jörgens ; translated by G.F. Roach
出版情報: Boston : Pitman Advanced Pub. Program, c1982  x, 379 p. ; 24 cm
シリーズ名: Surveys and reference works in mathematics / main editors, A. Jeffrey, R.G. Douglas ; [7]
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4.

図書

図書
Hermann König
出版情報: Basel ; Boston : Birkhäuser Verlag, 1986  262 p. ; 24 cm
シリーズ名: Operator theory : advances and applications ; v. 16
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5.

図書

図書
by Victor G. Kravchenko and Georgii S. Litvinchuk
出版情報: Dordrecht ; Boston : Kluwer Academic Publishers, c1994  xvi, 288 p. ; 25 cm
シリーズ名: Mathematics and its applications ; v. 289
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6.

図書

図書
G.O. Okikiolu
出版情報: London ; New York : Academic Press, 1971  ix, 522 p. ; 24 cm
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7.

図書

図書
von S.G. Michlin und S. Prössdorf
出版情報: Berlin : Akademie-Verlag, 1980  xii, 514 p. ; 25 cm
シリーズ名: Mathematische Lehrbücher und Monographien ; Abt. 2 . Mathematische Monographien ; Bd. 52
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8.

図書

図書
Yves Meyer
出版情報: Paris : Hermann, c1990  xii, [217]-381 p. ; 24 cm
シリーズ名: Ondelettes et opérateurs ; 2
Actualités mathématiques
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9.

図書

図書
M.A. Krasnoselskii ... [et al.] ; translated by T. Ando
出版情報: Leyden : Noordhoff International Publishing, c1976  xv, 520 p. ; 24 cm
シリーズ名: Monographs and textbooks on mechanics of solids and fluids ; Mechanics analysis
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10.

図書

図書
von I. Gohberg und N. Krupnik ; in deutscher Sprache herausgegeben von E. Meister ; deutsche Übersetzung von B. Schüppel
出版情報: Basel ; Boston : Birkhäuser, 1979  379 p. ; 26 cm
シリーズ名: Lehrbücher und Monographien aus dem Gebiete der exakten Wissenschaften ; Mathematische Reihe ; Bd. 63
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