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

Robert J. Taggart

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arXiv · 0705.4510

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

Robert J. Taggart

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Abstract

Suppose that T_t is a symmetric diffusion semigroup on L^2(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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BibTeX RIS

Robert J. Taggart. 2008-02-28. Pointwise convergence for semigroups in vector-valued $L^p$ spaces. https://arxiv.org/abs/0705.4510

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