ALMOST EVERYWHERE CONVERGENCE OF GENERALIZED ERGODIC TRANSFORMS FOR INVERTIBLE POWER-BOUNDED OPERATORS IN LP

被引：4
|
作者：
Cuny, Christophe [1 ]
机构：
[1] Ecole Cent Paris, Lab MAS, F-92295 Chatenay Malabry, France
来源：
COLLOQUIUM MATHEMATICUM | 2011年 / 124卷 / 01期
关键词：
Berkson-Gillespie spectral integral; L-P spaces; ergodic transforms; almost everywhere convergence; HILBERT TRANSFORM; THEOREM;
D O I：
10.4064/cm124-1-5
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We show that some results of Gaposhkin about a.e. convergence of series associated to a unitary operator U acting on L-2 (X, Sigma, mu) (mu is a sigma-finite measure) may be extended to the case where U is an invertible power-bounded operator acting on L-P(X, Sigma, mu), p>1. The proofs make use of the spectral integration initiated by Berkson-Gillespie and, more specifically, of recent results of the author.
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页码：61 / 77
页数：17
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