关键词: 截断极大算子, 连续性, L^p(Rⁿ)→L^p(Rⁿ)范数

Abstract: This paper focuses on the continuity of L^p(Rⁿ)→L^p(Rⁿ)-norm of the truncated Hardy-Littlewood maximal operator M^b_a with two truncation parameters a and b. We first, respectively, present the left semi-continuity and right semicontinuity of ‖M^b_a‖_{L^p(Rⁿ)→L^p(Rⁿ)} with respect to θ=b/a, and then the continuity of ‖M^b_a‖_{L^p(Rⁿ)→L^p(Rⁿ)} is extended to infinity.

Key words: truncated maximal operator, continuity, L^p(Rⁿ)→L^p(Rⁿ)-norm