Vector Valued Differentiation Theorems for Multiparameter Additive Processes in Lp Spaces |
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Authors: | Sato Ryotaro |
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Institution: | (1) Department of Mathematics, Faculty of Science, Okayama University, Okayama, 700, Japan |
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Abstract: | Let X be a Banach space and (,,µ) be a -finite measure space. We consider a strongly continuous d-dimensional semigroup T={T(u):u=(u1,..., ud, ui >0, 1 i d} of linear contractions on Lp((,,µ); X), with 1 p<. In this paper differentiation theorems are proved for d-dimensional bounded processes in Lp((,,µ); X) which are additive with respect to T. In the theorems below we assume that each T(u) possesses a contraction majorant P(u) defined on Lp((,,µ); R), that is, P(u) is a positive linear contraction on Lp((,,µ); R) such that T(u)f(w) P(u)f(·)() almost everywhere on for all f Lp((,,µ); X). |
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Keywords: | Vector valued local ergodic theorem and differentiation theorem multiparameter additive process contraction majorant |
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