On the Korányi Spherical maximal function on Heisenberg groups

2022/04/01 by Srivastava, Rajula · 2 citations
#43A80 Secondary: 43A15 #58J40 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #Primary: 42B25

paper · doi:10.48550/arxiv.2204.00695

Abstract

We prove L^p→ L^q estimates 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→ L^q estimates for spherical means over the Korányi sphere, which can be used to improve the sparse domination bounds for the associated lacunary maximal operator.

Cited by

• Problems on spherical maximal functions
• Lacunary δ-Discretised Spherical Maximal Operators

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