Report 30/2005: Real Analysis, Harmonic Analysis and Applications to PDE (July 3rd -- July 9th, 2005 (0527))
type: Item
instance of: scholarly article
title: Report 30/2005: Real Analysis, Harmonic Analysis and Applications to PDE (July 3rd -- July 9th, 2005 (0527))
zbMATH Open document ID: 1106.42300
DOI: 10.4171/OWR/2005/30
published in: Oberwolfach Reports
publication date: 2007-03-14T00:00:00Z
full work available at URL: http://www.ems-ph.org/journals/show_abstract.php
review text: Summary: There have been important developments in the last few years in the point-of-view and methods of harmonic analysis, and at the same time significant concurrent progress in the application of these to partial differential equations and related subjects. The conference brought together experts and young scientists working in these two directions, with the objective of furthering these important interactions. Introduction: Major areas and results represented at the workshop are: I. Methods in harmonic analysis (a) Multilinear analysis: this is an outgrowth of the method of `tile decomposition' which has been so successful in solving the problems of the bilinear Hilbert transform. Recent progress involves the control of maximal trilinear operators and an extension of the Carleson-Hunt theorem. (b) Geometry of sets in \(\mathbb{R}^d\): This includes recent progress on the interaction of Fourier analysis and geometric combinatorics related to the Falconer distance problem. (c) Singular integrals: A break trough has been obtained on singular integrals on solvable Iwasawa AN- groups, which require a new type of Calderón-Zygmund decomposition, since the underlying spaces have exponential volume growth. Further significant progress involves the theory of operator-valued Calderón-Zygmund operators and their connection to maximal regularity of evolution equations. (d) Oscillatory integrals, Fourier integral operators and Maximal operators: This includes estimates of maximal operators related to polynomial polyhedra and their relations with higher dimensional complex analysis, sharp estimates for maximal operators associated to hypersurfaces in \(\mathbb{R}^3\), estimates for degenerate Radon transforms and linear and bilinear estimates for oscillatory integral operators, as well as optimal Sobolev regularity for Fourier integral operators. II. Applications to P.D.E. \parindent=6mm \begin{itemize}\item[(a)]Dispersive linear and nonlinear equations: Far reaching new appr…
Mathematics Subject Classification ID: 42-06
Mathematics Subject Classification ID: 43-06
Mathematics Subject Classification ID: 22-06
Mathematics Subject Classification ID: 35-06
Mathematics Subject Classification ID: 00B05
zbMATH DE Number: 5133455
MaRDI profile type: Publication
OpenAlex ID: W2046527657
description: scientific article; zbMATH DE number 5133455