**Contemporary Mathematics**

Volume: 612;
2014;
178 pp;
Softcover

MSC: Primary 31; 35; 42; 46; 47;

Print ISBN: 978-0-8218-9433-0

Product Code: CONM/612

List Price: $78.00

AMS Member Price: $62.40

MAA Member Price: $70.20

**Electronic ISBN: 978-1-4704-1525-9
Product Code: CONM/612.E**

List Price: $78.00

AMS Member Price: $62.40

MAA Member Price: $70.20

# Harmonic Analysis and Partial Differential Equations

Share this page *Edited by *
*Patricio Cifuentes; José García-Cuerva; Gustavo Garrigós; Eugenio Hernández; José María Martell; Javier Parcet; Keith M. Rogers; Alberto Ruiz; Fernando Soria; Ana Vargas*

This volume contains the Proceedings of the
9th International Conference on Harmonic Analysis and Partial
Differential Equations, held June 11–15, 2012, in El Escorial,
Madrid, Spain.

Included in this volume is the written version of the mini-course
given by Jonathan Bennett on Aspects of Multilinear Harmonic Analysis
Related to Transversality. Also included, among other papers, is a
paper by Emmanouil Milakis, Jill Pipher, and Tatiana Toro, which
reflects and extends the ideas presented in the mini-course on
Analysis on Non-smooth Domains delivered at the conference by Tatiana
Toro.

The topics of the contributed lectures cover a wide range of the
field of Harmonic Analysis and Partial Differential Equations and
illustrate the fruitful interplay between the two subfields.

#### Readership

Graduate students and research mathematicians interested in harmonic analysis and partial differential equations.

# Table of Contents

## Harmonic Analysis and Partial Differential Equations

- Introduction vii8 free
- Aspects of multilinear harmonic analysis related to transversality 110 free
- 1. Introduction 110
- 2. The linear restriction theory for the Fourier transform 211
- 3. The bilinear restriction theory: the emergence of transversality 514
- 4. Multilinear transversality and the multilinear restriction theory 817
- 5. Transversal multilinear harmonic analysis: a bigger picture 1726
- References 2534

- Multi-frequency Calderón-Zygmund analysis and connexion to Bochner-Riesz multipliers 2938
- Sharp Bounds for 𝑡-Haar Multipliers on 𝐿² 4554
- Spectra of Frame Operators with Prescribed Frame Norms 6574
- Regularity criteria for Hall-magnetohydrodynamics and the space-time Monopole equation in Lorenz gauge 8190
- The 𝐴₂ theorem: Remarks and complements 91100
- An invitation to harmonic analysis associated with semigroups of operators 107116
- 1. A sample case 107116
- 2. What is a framework to setup the theory? 110119
- 3. BMO spaces, interpolation and duality 112121
- 4. Hörmander-Mihlin multipliers and Riesz transforms 114123
- 5. What are Calderón-Zygmund singular integrals? 117126
- 6. Metric on noncommutative measure spaces 119128
- References 120129

- The higher order regularity Dirichlet problem for elliptic systems in the upper-half space 123132
- Perturbations of elliptic operators in chord arc domains 143152
- Cauchy non-integral formulas 163172