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Keywords:
sharp constant; truncated maximal operator; strong maximal operator
sharp constant; truncated maximal operator; strong maximal operator
Summary:
This paper focuses on the operator norm of the truncated Hardy-Littlewood maximal operator $M^b_a$ and the strong truncated Hardy-Littlewood maximal operator $\widetilde {M}^{\boldsymbol {b}}_{\boldsymbol {a}}$, respectively. We first present the $L^1$-norm of $M^b_a$, and then the $L^1$-norm of $\widetilde {M}^{\boldsymbol {b}}_{\boldsymbol {a}}$ is given. Our study may have some enlightening significance for the research on sharp constant for the classical Hardy-Littlewood maximal inequality.
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