Harmonic Analysis and Partial Differential Equations.

Harmonic Analysis and Partial Differential Equations.

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Bibliographic Details
Author / Creator: Cifuentes, Patricio.
Other Authors / Creators:García-Cuerva, José.
Garrigós, Gustavo.
Hernandez, Eugenio.
Parcet, Javier.
Ruiz, Alberto.
Soria, Fernando.
Vargas, Ana.
Martell, Jose Maria.
Rogers, Keith M.
Format: eBook Electronic
Language:English
Imprint: Providence : American Mathematical Society, 2014.
Series:Contemporary Mathematics
Subjects:
Harmonic analysis > Congresses.
Differential equations, Partial > Congresses.
Electronic books.
Local Note:Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2022. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
Online Access:Click to View
Table of Contents:
  • Intro
  • Introduction
  • Aspects of multilinear harmonic analysis related to transversality
  • 1. Introduction
  • 2. The linear restriction theory for the Fourier transform
  • 3. The bilinear restriction theory: the emergence of transversality
  • 4. Multilinear transversality and the multilinear restriction theory
  • 5. Transversal multilinear harmonic analysis: a bigger picture
  • References
  • Multi-frequency Calderón-Zygmund analysis and connexion to Bochner-Riesz multipliers
  • 1. Notations and preliminaries
  • 2. Unweighted estimates for multi-frequency Calderón-Zygmund operators
  • 3. Weighted estimates for multi-frequency Calderón-Zygmund operators
  • 4. Connexion to Bochner-Riesz multipliers
  • References
  • Sharp Bounds for -Haar Multipliers on ²
  • 1. Introduction
  • 2. Preliminaries
  • 3. Main tools
  • 4. Haar Multipliers
  • 5. Appendix
  • References
  • Spectra of Frame Operators with Prescribed Frame Norms
  • 1. Introduction
  • 2. Background results about Schur-Horn type theorems
  • 3. Spectral set
  • References
  • Regularity criteria for Hall-magnetohydrodynamics and the space-time Monopole equation in Lorenz gauge
  • 1. Introduction
  • 2. Proof of Theorem 1.1
  • 3. Proof of Theorem 1.3
  • 4. Proof of Theorem 1.7
  • Acknowledgments
  • References
  • The ₂ theorem: Remarks and complements
  • 1. Introduction
  • 2. Detailed outline of the lower-left route
  • 3. Proof of Lerner's formula
  • 4. Sharpness of the weak (1,1) estimate
  • 5. A direct verification of the testing conditions
  • 6. The two-weight 1 theorem for positive operators
  • References
  • An invitation to harmonic analysis associated with semigroups of operators
  • 1. A sample case
  • 2. What is a framework to setup the theory?
  • 3. BMO spaces, interpolation and duality
  • 4. Hörmander-Mihlin multipliers and Riesz transforms.
  • 5. What are Calderón-Zygmund singular integrals?
  • 6. Metric on noncommutative measure spaces
  • References
  • The higher order regularity Dirichlet problem for elliptic systems in the upper-half space
  • 1. Introduction
  • 2. Preliminaries
  • 3. Poisson kernels
  • 4. The Dirichlet problem with data in higher order Sobolev spaces
  • 5. Examples of boundary problems of mathematical physics
  • References
  • Perturbations of elliptic operators in chord arc domains
  • 1. Introduction
  • 2. Preliminaries
  • 3. Main Result
  • References
  • Cauchy non-integral formulas
  • 1. Introduction
  • 2. Carleson estimates of operators
  • 3. Proof of the Cauchy formula
  • 4. Applications to the Neumann and Dirichlet problem
  • References.

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