Noncommutative maximal ergodic theorems for spherical means on the\n Heisenberg group

2016/11/05 by Guixiang Hong, Hong, Guixiang · 2 citations
Mathematics · #Advanced Mathematical Physics Problems #Mathematical Analysis and Transform Methods #Advanced Harmonic Analysis Research

paper · pdf · doi:10.48550/arxiv.1611.01651

Abstract

We prove maximal ergodic theorems for spherical averages on the Heisenberg\ngroups acting on L_p spaces over measure spaces not necessarily commutative,\nthat is, on noncommutative L_p spaces. The scale of p is optimal in the\nreduced Heisenberg group case. We also obtain the corresponding individual\nergodic theorems and differential theorems in the noncommutative setting. The\nresults can be regarded as noncommutative analogues of Nevo-Thangavelu's\nergodic theorems. The approach of proof involves recent developments in\nnoncommutative L_p spaces and in noncommutative harmonic analysis, in\naddition to the spectral theory used in the commutative setting.\n

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