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- W4287980002 abstract "In this paper we investigate the $L^p$ boundedness of the lacunary maximal function $ M_{Ha}^{lac} $ associated to the spherical means $ A_r f$ taken over Koranyi spheres on the Heisenberg group. Closely following an approach used by M. Lacey in the Euclidean case, we obtain sparse bounds for these maximal functions leading to new unweighted and weighted estimates. The key ingredients in the proof are the $L^p$ improving property of the operator $A_rf$ and a continuity property of the difference $A_rf-tau_y A_rf$, where $tau_yf(x)=f(xy^{-1})$ is the right translation operator." @default.
- W4287980002 created "2022-07-26" @default.
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- W4287980002 date "2019-12-24" @default.
- W4287980002 modified "2023-09-29" @default.
- W4287980002 title "On the lacunary spherical maximal function on the Heisenberg group" @default.
- W4287980002 doi "https://doi.org/10.48550/arxiv.1912.11302" @default.
- W4287980002 hasPublicationYear "2019" @default.
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