This paper focuses on the operator norm of the truncated Hardy-Littlewood maximal operator M a b and the strong truncated Hardy-Littlewood maximal operator \(\widetilde{M}_{\boldsymbol{a}}^{\boldsymbol{b}}\) , respectively. We first present the L1-norm of M a b , and then the L1-norm of \(\widetilde{M}_{\boldsymbol{a}}^{\boldsymbol{b}}\) is given. Our study may have some enlightening significance for the research on sharp constant for the classical Hardy-Littlewood maximal inequality.
