Classical and Multilinear Harmonic Analysis: Frontmatter
By Camil Muscalu, Wilhelm Schlag. 2013
216 citations recorded by the source corpus.
This two-volume text in harmonic analysis introduces a wealth of analytical results and techniques. It is largely self-contained and will be useful to graduate students and researchers in both pure and applied analysis. Numerous exercises and problems make the text suitable for self-study and the classroom alike. This first volume starts with classical one-dimensional topics: Fourier series; harmonic functions; Hilbert transform. Then the higher-dimensional Calderon–Zygmund and Littlewood–Paley theories are developed. Probabilistic methods and their applications are discussed, as are applications of harmonic analysis to partial differential equations. The volume concludes with an introduction to the Weyl calculus. The second volume goes beyond the classical to the highly contemporary and focuses on multilinear aspects of harmonic analysis: the bilinear Hilbert transform; Coifman–Meyer theory; Carleson's resolution of the Lusin conjecture; Calderon's commutators and the Cauchy integral on Lipschitz curves. The material in this volume has not previously appeared together in book form.
Subfields: Applied Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/1501c1cccd7dc19c4ba634c7d7999994e546ee18
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Applied Mathematics
In Mathematical Physics
Citations in the corpus
- Hörmander type theorems for multi-linear and multi-parameter Fourier multiplier operators with limited smoothness (2014, background): “The difficult part of their proof is in the quasi-Banach casewhen 0 < r ≤ 1where the standard duality argument for the paraproducts does not work (see also [20]).”
- Global regularity for 2D Muskat equations with finite slope (2015, background): “puting a Caldero´n commutator applied to the identity (cf. (2.3) below). However, when f′ is merely bounded, while the Caldero´n commutator maps Lp → Lp for p∈ (1,∞), the endpoint L∞ inequality fails [MS13]. Moreover, since we are in 1D the x-derivative ofventers the estimates (we cannot use incompr”
- Paracontrolled approach to the three-dimensional stochastic nonlinear wave equation with quadratic nonlinearity (2018, background): “1) in [67]) and the transference principle [26, Theorem 3].”
- Multiple Vector Valued Inequalities via the Helicoidal Method (2015, methodology): “The detailed reduction can be found in [MS13], Chapter 6.”
- Rough Bilinear Singular Integrals (2015, background): “General facts about bilinear operators can be found in [23, Chapter 13], [14, Chapter 7], and [24].”