Pointwise convergence for semigroups in vector-valued L^p spaces

2007/05/31 by Robert Taggart, Robert J. Taggart, Taggart, Robert J.
Mathematics · #47D03 #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Spectral Theory (math.SP) #math.FA #math.SP #msc:47D03

paper · pdf · doi:10.48550/arxiv.0705.4510

In version2 we correct the error present in version 1 as well as removing one of the hypotheses of the main theorem. Section 2 is also rewritten

openalex publication_date 2007/05/31 · arxiv created 2008/02/28 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Suppose that T_t is a symmetric diffusion semigroup on L²(X) and consider its tensor product extension to the Bochner space L^p(X,B), where B belongs to a certain broad class of UMD spaces. We prove a vector-valued version of the Hopf--Dunford--Schwartz ergodic theorem and show that this extends to a maximal theorem for analytic continuations of the semigroup's extension to L^p(X,B). As an application, we show that such continuations exhibit pointwise convergence.

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