This paper focuses on the continuity of Lp(Rn)→Lp(Rn)-norm of the truncated Hardy-Littlewood maximal operator Mba with two truncation parameters a and b. We first, respectively, present the left semi-continuity and right semicontinuity of ‖Mba‖Lp(Rn)→Lp(Rn) with respect to θ=b/a, and then the continuity of ‖Mba‖Lp(Rn)→Lp(Rn) is extended to infinity.
WU Jia
,
WEI Mingquan
,
YAN Dunyan
. Continuity of the Lp-norm of the truncated Hardy-Littlewood maximal operator[J]. Journal of University of Chinese Academy of Sciences, 2024
, 41(1)
: 28
-34
.
DOI: 10.7523/j.ucas.2021.0073
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