Mapping properties of the discrete fractional maximal operator in metric measure spaces

Toni Heikkinen, Juha Kinnunen, Juho Nuutinen, Heli Tuominen

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

This work studies boundedness properties of the fractional maximal operator on metric measure spaces under standard assumptions on the measure. The main motivation is to show that the fractional maximal operator has similar smoothing and mapping properties as the Riesz potential. Instead of the usual fractional maximal operator, we also consider a so-called discrete maximal operator which has better regularity. We study the boundedness of the discrete fractional maximal operator in Sobolev, Hölder, Morrey, and Campanato spaces. We also prove a version of the Coifman-Rochberg lemma for the fractional maximal function.

Original languageEnglish
Pages (from-to)693-712
Number of pages20
JournalKYOTO JOURNAL OF MATHEMATICS
Volume53
Issue number3
DOIs
Publication statusPublished - Sep 2013
MoE publication typeA1 Journal article-refereed

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