On some questions related to the maximal operator on variable Lp spaces

Research output: Contribution to journalArticlepeer-review

34 Scopus citations

Abstract

Let P(ℝn) be the class of all exponents p for which the Hardy- Littlewood maximal operator M is bounded on Lp(·) (ℝn). A recent result by T. Kopaliani provides a characterization of P in terms of the Muckenhoupttype condition A under some restrictions on the behavior of p at infinity. We give a different proof of a slightly extended version of this result. Then we characterize a weak type (p(·), p(·)) property of M in terms of A for radially decreasing p. Finally, we construct an example showing that p ε P(ℝn) does not imply p(·) - α ε P(ℝn) for all α < p- - 1. Similarly, p ε P(ℝn) does not imply αp(·) ε P(ℝn) for all a > 1/p-.

Original languageEnglish
Pages (from-to)4229-4242
Number of pages14
JournalTransactions of the American Mathematical Society
Volume362
Issue number8
DOIs
StatePublished - Aug 2010

Keywords

  • Maximal operator
  • Variable L spaces

Fingerprint

Dive into the research topics of 'On some questions related to the maximal operator on variable Lp spaces'. Together they form a unique fingerprint.

Cite this