On the maximal function associated to the spherical means on the heisenberg group

Bagchi, S and Hait, S and Roncal, L and Thangavelu, S (2021) On the maximal function associated to the spherical means on the heisenberg group. In: New York Journal of Mathematics, 27 . pp. 631-675.

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Abstract

In this paper we deal with lacunary and full versions of the spherical maximal function on the Heisenberg group Hn, for n ≥ 2. By suitable adaptation of an approach developed by M. Lacey in the Euclidean case, we obtain sparse bounds for these maximal functions, which lead to new unweighted and weighted estimates. In particular, we deduce the Lp boundedness, for 1 < p < ∞, of the lacunary maximal function associated to the spherical means on the Heisenberg group. In order to prove the sparse bounds, we establish Lp − Lq estimates for local (single scale) variants of the spherical means.

Item Type:	Journal Article
Publication:	New York Journal of Mathematics
Publisher:	University at Albany
Additional Information:	The copyright for this article belongs to University at Albany.
Keywords:	Heisenberg group; Lp-improving estimates; Sparse domination; Spherical means; Weighted theory
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	09 Mar 2023 06:26
Last Modified:	09 Mar 2023 06:26
URI:	https://eprints.iisc.ac.in/id/eprint/80883

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