Pointwise convergence for semigroups in vector-valued $L^p$ spaces
Functional Analysis
2008-02-28 v2 Spectral Theory
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.
Cite
@article{arxiv.0705.4510,
title = {Pointwise convergence for semigroups in vector-valued $L^p$ spaces},
author = {Robert J. Taggart},
journal= {arXiv preprint arXiv:0705.4510},
year = {2008}
}