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Title: On the Korányi spherical maximal function on Heisenberg groups

We prove$$L^p\rightarrow L^q$$LpLqestimates for the local maximal operator associated with dilates of the Kóranyi sphere in Heisenberg groups. These estimates are sharp up to endpoints and imply new bounds on sparse domination for the corresponding global maximal operator. We also prove sharp$$L^p\rightarrow L^q$$LpLqestimates for spherical means over the Korányi sphere, which can be used to improve the sparse domination bounds in (Ganguly and Thangavelu in J Funct Anal 280(3):108832, 2021) for the associated lacunary maximal operator.

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Springer Science + Business Media
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Journal Name:
Mathematische Annalen
Medium: X Size: p. 191-247
p. 191-247
Sponsoring Org:
National Science Foundation
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