Title: New directions in harmonic analysis on L-1
Authors: Spector, Daniel
應用數學系
Department of Applied Mathematics
Keywords: Sobolev inequalities;Riesz potentials;L-1 estimates
Issue Date: 1-Mar-2020
Abstract: The study of what we now call Sobolev inequalities has been studied for almost a century in various forms, while it has been eighty years since Sobolev's seminal mathematical contributions. Yet there are still things we do not understand about the action of integral operators on functions. This is no more apparent than in the L-1 setting, where only recently have optimal inequalities been obtained on the Lebesgue and Lorentz scale for scalar functions, while the full resolution of similar estimates for vector-valued functions is incomplete. The purpose of this paper is to discuss how some often overlooked estimates for the classical Poisson equation give an entry into these questions, to present the state of the art of what is known, and to survey some open problems on the frontier of research in the area. (C) 2019 Elsevier Ltd. All rights reserved.
URI: http://dx.doi.org/10.1016/j.na.2019.111685
http://hdl.handle.net/11536/153777
ISSN: 0362-546X
DOI: 10.1016/j.na.2019.111685
Journal: NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
Volume: 192
Begin Page: 0
End Page: 0
Appears in Collections:Articles