Weak differentiability for fractional maximal functions of general L-P functions on domains

Joao P. G. Ramos, Olli Saari*, Julian Weigt

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

Abstract

Let Omega subset of R-n be bounded a domain. We prove under certain structural assumptions that the fractional maximal operator relative to Omega maps L-p(Omega) -> W-1,W-p (Omega) for all p > 1, when the smoothness index alpha >= 1. In particular, the results are valid in the range p is an element of (1, n/(n - 1)] that was previously unknown. As an application, we prove an endpoint regularity result in the domain setting. (C) 2020 Elsevier Inc. All rights reserved.

Original languageEnglish
Article number107144
Number of pages25
JournalADVANCES IN MATHEMATICS
Volume368
DOIs
Publication statusPublished - 15 Jul 2020
MoE publication typeA1 Journal article-refereed

Keywords

  • Maximal function
  • Sobolev space
  • Spherical means
  • Domains
  • REGULARITY

Cite this