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Lebesgue space estimates for spherical maximal functions on Heisenberg groups
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Lebesgue space estimates for spherical maximal functions on Heisenberg groups
classification
math.CA
math.FA
keywords
groupsmaximalestimatesheisenbergoperatorsappliedassociatedbounds
read the original 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 M\'etivier groups.
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