Equivalence of operator norm for Hardy-Littlewood maximal operators and their truncated operators on Morrey spaces

Abstract

We will prove that for and , the central Morrey norm of the truncated centered Hardy-Littlewood maximal operator {{\displaystyle M}}_{\gamma }^c equals that of the centered Hardy-Littlewood maximal operator for all . When p = 1 and , it turns out that the weak central Morrey norm of the truncated centered Hardy-Littlewood maximal operator {{\displaystyle M}}_{\gamma }^c equals that of the centered Hardy-Littlewood maximal operator for all . Moreover, the same results are true for the truncated uncentered Hardy-Littlewood maximal operator. Our work extends the previous results of Lebesgue spaces to Morrey spaces.

Keywords

Hardy-Littlewood maximal function / truncated Hardy-Littlewood maximal function / Morrey norms / weak Morrey norms

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