Lebesgue space estimates for spherical maximal functions on Heisenberg groups

Abstract

We prove $L^p\to L^q$ estimates for local maximal operators associated with dilates of codimension two spheres in Heisenberg groups; these are sharp up to two endpoints. The results can be applied to improve currently known bounds on sparse domination for global maximal operators. We also consider lacunary variants, and extensions to Métivier groups.

arXiv comment29 pages, 1 figure. Minor revisions

References in corpus (6)

• Sharp weighted norm estimates beyond Calderón-Zygmund theory
• $L^p\to L^q$ bounds for spherical maximal operators
• Spherical maximal functions and fractal dimensions of dilation sets
• On the maximal function associated to the spherical means on the Heisenberg group
• Multi-scale sparse domination
• Annulus Maximal Averages on Variable Hyperplanes

Cited by in corpus (2)

• Multi-scale sparse domination
• $L^p-L^q$ estimates for the circular maximal operators on Heisenberg radial functions