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 𝑡-Haar Multipliers on 𝐿²

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 𝐴₂ 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 𝑇1 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