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1.

図書
図書
1. Fourier integrals in classical analysis. 2nd ed (: hardback)
Christopher D. Sogge
出版情報: Cambridge : Cambridge University Press, 2017  xiv, 334 p. ; 24 cm
シリーズ名: Cambridge tracts in mathematics ; 210
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2.

図書
図書
2. A primer on Fourier analysis for the geosciences (: pbk)
Robin Crockett
出版情報: Cambridge : Cambridge University Press, 2019  xiv, 176 p. ; 23 cm
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3.

図書
図書
3. Fourier analysis and nonlinear partial differential equations (: hbk ; : pbk)
Hajer Bahouri, Jean-Yves Chemin, Raphaël Danchin
出版情報: Heidelberg : Springer, c2011  xv, 523 p. ; 25 cm
シリーズ名: Die Grundlehren der mathematischen Wissenschaften ; 343
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目次情報: 続きを見る
Basic Analysis / 1：
Basic Real Anslysis / 1.1：
Holder and Convolution Inequslities / 1.1.1：
The Atomic Decomposition / 1.1.2：
Proof of Refined Young Inequslityp8 / 1.1.3：
A Bilinear Interpolation Theorem / 1.1.4：
A Linear Interpolation Result / 1.1.5：
The Hardy-Littlewood Maximal Function / 1.1.6：
The Fourier Transform / 1.2：
Fourier Transforms of Functions and the Schwartz Space / 1.2.1：
Tempered Distributions and the Fourier Transform / 1.2.2：
A Few Calculations of Fourier Transforms / 1.2.3：
Homogeneous Sobolev Spaces / 1.3：
Definition and Basic Properties / 1.3.1：
Sobolev Embedding in Lebesgue Spaces / 1.3.2：
The Limit Case Hd/2 / 1.3.3：
The Embedding Theorem in Hölder Spaces / 1.3.4：
Nonhomogeneous Sobolev Spaces on Rd / 1.4：
Embedding / 1.4.1：
A Density Theorem / 1.4.3：
Hardy Inequality / 1.4.4：
References and Remarks / 1.5：
Littlewood-Paley Theory / 2：
Functions with Compactly Supported Fourier Transforms / 2.1：
Bernstein-Type Lemmas / 2.1.1：
The Smoothing Effect of Heat Flow / 2.1.2：
The Action of a Diffeomorphism / 2.1.3：
The Effects of Some Nonlinear Functions / 2.1.4：
Dyadic Partition of Unity / 2.2：
Homogeneous Besov Spaces / 2.3：
Characterizations of Homogeneous Besov Spaces / 2.4：
Besov Spaces, Lebesgue Spaces, and Refined Inequalities / 2.5：
Homogeneous Paradifferential Calculus / 2.6：
Homogeneous Bony Decomposition / 2.6.1：
Action of Smooth Functions / 2.6.2：
Time-Space Besov Spaces / 2.6.3：
Nonhomogeneous Besov Spaces / 2.7：
Nonhomogeneous Paradifferential Calculus / 2.8：
The Bony Decomposition / 2.8.1：
The Paralinearization Theorem / 2.8.2：
Besov Spaces and Compact Embeddings / 2.9：
Commutator Estimates / 2.10：
Around the Space B&infty;,&infty;1 / 2.11：
Transport and Transport-Diffusion Equations / 2.12：
Ordinary Differential Equations / 3.1：
The Cauchy-Lipschitz Theorem Revisited / 3.1.1：
Estimates for the Flow / 3.1.2：
A Blow-up Criterion for Ordinary Differential Equations / 3.1.3：
Transport Equations: The Lipschitz Case / 3.2：
A Priori Estimates in General Besov Spaces / 3.2.1：
Refined Estimates in Besov Spaces with Index 0 / 3.2.2：
Solving the Transport Equation in Besov Spaces / 3.2.3：
Application to a Shallow Water Equation / 3.2.4：
Losing Estimates for Transport Equations / 3.3：
Linear Loss of Regularity in Besov Spaces / 3.3.1：
The Exponential Loss / 3.3.2：
Limited Loss of Regularity / 3.3.3：
A Few Applications / 3.3.4：
Transport-Diffusion Equations / 3.4：
A Priori Estimates / 3.4.1：
Exponential Decay / 3.4.2：
Quasilinear Symmetric Systems / 3.5：
Definition and Examples / 4.1：
Linear Symmetric Systems / 4.2：
The Well-posedness of Linear Symmetric Systems / 4.2.1：
Finite Propagation Speed / 4.2.2：
Further Well-posedness Results for Linear Symmetric Systems / 4.2.3：
The Resolution of Quasilinear Symmetric Systems / 4.3：
Paralinearization and Energy Estimates / 4.3.1：
Convergence of the Scheme / 4.3.2：
Completion of the Proof of Existence / 4.3.3：
Uniqueness and Continuation Criterion / 4.3.4：
Data with Critical Regularity and Blow-up Criteria / 4.4：
Critical Besov Regularity / 4.4.1：
A Refined Blow-up Crndition / 4.4.2：
Continuity of the Flow Map / 4.5：
The Incompressible Navier-Stokes System / 4.6：
Basic Facts Concerning the Navier-Stokes System / 5.1：
Well-posedness in Sobolev Spaces / 5.2：
A General Result / 5.2.1：
The Behavior of the Hd/2-1 Norm Near 0 / 5.2.2：
Results Related to the Structure of the System / 5.3：
The Particular Case of Dimension Two / 5.3.1：
The Case of Dimension Three / 5.3.2：
An Elementary Lp Approach / 5.4：
The Endpoint Space for Picard's Scheme / 5.5：
The Use of the L1-smoothing Effect of the Heat Flow / 5.6：
The Cannone-Meyer-Planchon Theorem Revisited / 5.6.1：
The Flow of the Solutions of the Navier-Stokes System / 5.6.2：
Anisotropic Viscosity / 5.7：
The Case of L2 Data with One Vertical Derivative in L2 / 6.1：
A Global Existence Result in Anisotropic Besov Spaces / 6.2：
Anisotropic Localization in Fourier Space / 6.2.1：
The Functional Framework / 6.2.2：
Statement of the Main Result / 6.2.3：
Some Technical Lemmas / 6.2.4：
The Proof of Existence / 6.3：
The Proof of Uniqueness / 6.4：
Euler System for Perfect Incompressible Fluids / 6.5：
Local Well-posedness Results for Inviscid Fluids / 7.1：
The Biot-Savart Law / 7.1.1：
Estimates for the Pressure / 7.1.2：
Another Formulation of the Euler System / 7.1.3：
Local Existence of Smooth Solutions / 7.1.4：
Uniqueness / 7.1.5：
Continuation Criteria / 7.1.6：
Global Existence Results in Dimension Two / 7.2：
Smooth Solutions / 7.2.1：
The Borderline Case / 7.2.2：
The Yudovich Theorem / 7.2.3：
The Inviscid Limit / 7.3：
Regularity Results for the Navier-Stokes System / 7.3.1：
The Smooth Case / 7.3.2：
The Rough Case / 7.3.3：
Viscous Vortex Patches / 7.4：
Results Related to Striated Regularity / 7.4.1：
A Stationary Estimate for the Velocity Field / 7.4.2：
Uniform Estimates for Striated Regularity / 7.4.3：
A Global Convergence Result for Striated Regularity / 7.4.4：
Application to Smooth Vortex Patches / 7.4.5：
Strichartz Estimates and Applications to Semilinear Dispersive Equations / 7.5：
Examples of Dispersive Estimates / 8.1：
The Dispersive Estimate for the Free Transport Equation / 8.1.1：
The Dispersive Estimates for the Schrdillger Equation / 8.1.2：
Integral of Oscillating Functions / 8.1.3：
Dispersive Estimates for the Wave Equation / 8.1.4：
The L2 Boundedness of Some Fourier Integral Operators / 8.1.5：
Billnear Methods / 8.2：
The Duality Method and the TT* Argument / 8.2.1：
Strichartz Estimates: The Case q > 2 / 8.2.2：
Strichartz Estimates: The Endpoint Case q = 2 / 8.2.3：
Application to the Cubic Semilinear Schrödinger Equation / 8.2.4：
Strichartz Estimates for the Wave Equation / 8.3：
The Basic Strichartz Estimate / 8.3.1：
The Refined Strichartz Estimate / 8.3.2：
The Qulntic Wave Equation in R3 / 8.4：
The Cubic Wave Equation in R3 / 8.5：
Solutions in H1 / 8.5.1：
Local and Global Well-posedness for Rough Data / 8.5.2：
The Nonlinear Interpolation Method / 8.5.3：
Application to a Class of Semilinear Wave Equations / 8.6：
Smoothing Effect in Quasilinear Wave Equations / 8.7：
A Well-posedness Result Based on an Energy Method / 9.1：
The Main Statement and the Strategy of its Proof / 9.2：
Refined Paralinearization of the Wave Equation / 9.3：
Reduction to a Microlocal Strichartz Estimate / 9.4：
Microlocal Strichartz Estimates / 9.5：
A Rather General Statement / 9.5.1：
Geometrical Optics / 9.5.2：
The Solution of the Eikonal Equation / 9.5.3：
The Transport Equation / 9.5.4：
The Approximation Theorem / 9.5.5：
The Proof of Theorem 9.16 / 9.5.6：
The Compressible Navier-Stokes System / 9.6：
About the Model / 10.1：
General Overview / 10.1.1：
The Barotropic Navier-Stokes Equations / 10.1.2：
Local Theory for Data with Critical Regularity / 10.2：
Scaling Invariance and Statement of the Main Result / 10.2.1：
Existence of a Local Solution / 10.2.2：
A Continuation Criterion / 10.2.4：
Local Theory for Data Bounded Away from the Vacuum / 10.3：
A Priori Estimates for the Linearized Momentum Equation / 10.3.1：
Global Existence for Small Data / 10.3.2：
Statement of the Results / 10.4.1：
A Spectral Analysis of the Linearized Equation / 10.4.2：
A Prioli Estimates for the Linearized Equation / 10.4.3：
Proof of Global Existence / 10.4.4：
The Incompressible Limit / 10.5：
Main Results / 10.5.1：
The Case of Small Data with Critical Regularity / 10.5.2：
The Case of Large Data with More Regularity / 10.5.3：
References / 10.6：
List of Notations
Index
Basic Analysis / 1：
Basic Real Anslysis / 1.1：
Holder and Convolution Inequslities / 1.1.1：
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