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- W2040393319 abstract "Let H = H n = C n × R denote the Heisenberg group, and let σ r denote the normalized Lebesgue measure on the sphere {( z , 0): | z |= r }. Let ( X , B , m ) be a standard Borel probability space on which H acts measurably and ergodically by measure preserving transformations, and let π ( σ r ) denote the operator canonically associated with σ r on L p ( X ). We prove maximal and pointwise ergodic theorems in L p , for radial averages σ r on the Heisenberg group H n , n >1. The results are best possible for actions of the reduced Heisenberg group. The method of proof is to use the spectral theory of the Banach algebra of radial measures on the group and decay estimates for its characters to establish maximal inequalities using spectral methods, in particular Littlewood–Paley–Stein square-functions and analytic interpolation." @default.
- W2040393319 created "2016-06-24" @default.
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- W2040393319 date "1997-05-01" @default.
- W2040393319 modified "2023-09-26" @default.
- W2040393319 title "Pointwise Ergodic Theorems for Radial Averages on the Heisenberg Group" @default.
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- W2040393319 doi "https://doi.org/10.1006/aima.1997.1641" @default.
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