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

2 Citations (Scopus)

Abstract

Let Ω⊂R n be bounded a domain. We prove under certain structural assumptions that the fractional maximal operator relative to Ω maps L p(Ω)→W 1,p(Ω) for all p>1, when the smoothness index α≥1. In particular, the results are valid in the range p∈(1,n/(n−1)] that was previously unknown. As an application, we prove an endpoint regularity result in the domain setting.

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

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