A necessary condition for the boundedness of the maximal operator on Lp(·) over reverse doubling spaces of homogeneous type

Research output: Contribution to journalArticlepeer-review

8 Downloads (Pure)

Abstract

Let (X,d,μ) be a space of homogeneous type and p(·):X→[1,∞] be a variable exponent. We show that if the measure μ is Borel-semiregular and reverse doubling, then the condition essinfx∈Xp(x)>1 is necessary for the boundedness of the Hardy–Littlewood maximal operator M on the variable Lebesgue space Lp(·)(X,d,μ).
Original languageEnglish
Number of pages8
JournalAnalysis Mathematica
Early online date2 Oct 2024
DOIs
Publication statusE-pub ahead of print - 2 Oct 2024

Keywords

  • 28C15
  • 42B25
  • 46E30
  • Borel-semiregular measure
  • reverse doubling condition
  • space of homogeneous type
  • The Hardy–Littlewood maximal operator
  • variable Lebesgue space

Cite this