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

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.