Ganguly, P and Thangavelu, S (2021) On the lacunary spherical maximal function on the Heisenberg group. In: Journal of Functional Analysis, 280 (3).
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Abstract
In this paper we investigate the Lp boundedness of the lacunary maximal function MHnlac associated to the spherical means Arf 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 Lp improving property of the operator Arf and a continuity property of the difference Arf��yArf, where �yf(x)=f(xy�1) is the right translation operator. © 2020 Elsevier Inc.
| Item Type: | Journal Article |
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| Publication: | Journal of Functional Analysis |
| Publisher: | Academic Press Inc. |
| Additional Information: | the copyright this belongs to Academic Press Inc. |
| Keywords: | Heisenberg group; Koranyi sphere; Lp-improving estimates; Lacunary spherical means; Sparse domination; Weighted theory Heisenberg group; Koranyi sphere; Lp-improving estimates; Lacunary spherical means; Sparse domination; Weighted theory |
| Department/Centre: | Division of Physical & Mathematical Sciences > Mathematics |
| Date Deposited: | 30 Dec 2021 04:33 |
| Last Modified: | 30 Dec 2021 04:33 |
| URI: | http://eprints.iisc.ac.in/id/eprint/67259 |
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