Multilinear singular integrals.
type: Item
instance of: scholarly article
title: Multilinear singular integrals.
zbMATH Open document ID: 1035.42011
author: Christoph Thiele
published in: Publicacions Matemàtiques
publication date: 2002-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/41615
review text: In this survey the author describes some recent results (and new proofs of existing results) concerning multilinear singular integrals such as the bilinear Hilbert transform, as well as related objects such as the Carleson maximal operator. In particular, the method of phase space decomposition (using truncations in both frequency space and physical space, not necessarily centered around the frequency origin, and thus generalizing Littlewood-Paley theory) to pass from these operators to a dyadically decomposed model operator is emphasized as playing an important role for the multilinear \(L^p\) theory of operators which obey a certain type of modulation symmetry. Further topics discussed include the change in phase space decompositions necessary to handle the bilinear Hilbert transform. The treatment of the Carleson operator is done in some detail, but most of the other operators are discussed in heuristic terms only. Finally, a discussion of the relationship between these operators and the eigenfunctions of one-dimensional Schrödinger operators is discussed.
Mathematics Subject Classification ID: 42B20
zbMATH DE Number: 1881292
zbMATH Keywords: Carleson operator
zbMATH Keywords: bilinear Hilbert transform
zbMATH Keywords: phase space
zbMATH Keywords: Littlewood-Paley decomposition
zbMATH Keywords: multilinear operators
zbMATH Keywords: Schrödinger operator
reviewed by: Terence Tao
MaRDI profile type: Publication
OpenAlex ID: W2143245836
DOI: 10.5565/PUBLMAT_ESCO02_11
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description: scientific article; zbMATH DE number 1881292