Lebesgue Space Estimates for Spherical Maximal Functions on Heisenberg Groups. (11th September 2021)

• Record Type: Journal Article
• Authors: Roos, Joris; Seeger, Andreas; Srivastava, Rajula
• Is Part Of: International mathematics research notices. Volume 2022:Number 24(2022)
• Page Start: 19222
• Page End: 19257
• Publication Date: 2021-09-11
• Subjects: Mathematics -- Periodicals; 510
• DOI: 10.1093/imrn/rnab246
• Languages: English
• ISSNs: 1073-7928

Abstract

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.