Maximal Operator in Variable Exponent Lebesgue Spaces on Unbounded Quasimetric Measure Spaces

  • Tomasz Adamowicz
  • Petteri Harjulehto
  • Peter Hästö

Abstract

We study the Hardy-Littlewood maximal operator $M$ on $L^{p({\cdot})}(X)$ when $X$ is an unbounded (quasi)metric measure space, and $p$ may be unbounded. We consider both the doubling and general measure case, and use two versions of the $\log$-Hölder condition. As a special case we obtain the criterion for a boundedness of $M$ on $L^{p({\cdot})}({\mathsf{R}^n},\mu)$ for arbitrary, possibly non-doubling, Radon measures.
Published
2015-03-04
How to Cite
Adamowicz, T., Harjulehto, P., & Hästö, P. (2015). Maximal Operator in Variable Exponent Lebesgue Spaces on Unbounded Quasimetric Measure Spaces. MATHEMATICA SCANDINAVICA, 116(1), 5-22. https://doi.org/10.7146/math.scand.a-20448
Section
Articles