A note on maximal operators related to Laplace-Bessel differential operators on variable exponent Lebesgue spaces

KAYA E.

Open Mathematics, vol.19, no.1, pp.306-315, 2021 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 19 Issue: 1
  • Publication Date: 2021
  • Doi Number: 10.1515/math-2021-0041
  • Journal Name: Open Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, Directory of Open Access Journals
  • Page Numbers: pp.306-315
  • Keywords: B-maximal operator, Generalized translation operator, Singular integrals, Variable exponent Lebesgue spaces
  • Bilecik Şeyh Edebali University Affiliated: No

Abstract

In this paper, we consider the maximal operator related to the Laplace-Bessel differential operator (B-maximal operator) on Lp(middot;)γ(ℝnk,+) variable exponent Lebesgue spaces. We will give a necessary condition for the boundedness of the B-maximal operator on variable exponent Lebesgue spaces. Moreover, we will obtain that the B-maximal operator is not bounded on Lp(middot;)γ(ℝnk,+) variable exponent Lebesgue spaces in the case of p- = 1. We will also prove the boundedness of the fractional maximal function associated with the Laplace-Bessel differential operator (fractional B-maximal function) on Lp(middot;)γ(ℝnk,+) variable exponent Lebesgue spaces.