Hardy–Littlewood maximal operators and Hausdorff operators on p-adic block spaces with variable exponents

Abstract

In this paper, we established some sufficient conditions for the boundedness of the Hardy–Littlewood maximal operators and the Hausdorff operators on $ p $-adic Herz spaces and $ p $-adic local block spaces with variable exponents. In particular, the boundedness of the $ p $-adic maximal commutator operators, the $ p $-adic Hardy–Littlewood average operators, and the $ p $-adic Hardy-Hilbert operators on such spaces was also discussed.

Keywords

• hardy–littlewood maximal operator
• maximal commutator operator
• hardy-type operators
• hausdorff operator
• herz space
• block space
• variable exponent
• $ p $-adic analysis