We consider two types of maximal operators. We prove that, under some conditions, each maximal operator is bounded from the classical dyadic martingale Hardy space Hp to the classical Lebesgue space Lp and from the variable dyadic martingale Hardy space Hp(·) to the variable Lebesgue space Lp(·). Using this, we can prove the boundedness of the Cesàro and Riesz maximal operator from Hp(·) to Lp(·) and from the variable Hardy-Lorentz space Hp(·),q to the variable Lorentz space Lp(·),q. As a consequence, we can prove theorems about almost everywhere and norm convergence.
- Cesàro and Riesz maximal operator
- Cesàro means
- Riesz means
- Variable Hardy spaces
- Variable Hardy-Lorentz spaces
ASJC Scopus subject areas
- Algebra and Number Theory