This is an announcement for the paper "Pointwise convergence for semigroups in vector-valued $L^p$ spaces" by Robert J Taggart.

Abstract: Suppose that T_t is a symmetric diffusion semigroup on L^2(X). We show that the tensor extension of T_t to L^p(X;B), where B belongs to a certain class of UMD spaces, exhibits pointwise convergence almost everywhere as t approaches zero. Our principal tools are vector-valued versions of maximal theorems due to Hopf--Dunford--Schwartz and Stein. These are proved using subpositivity and estimates on the bounded imaginary powers of the generator of T_t. An extension of these results to analytic continuations of T_t is also given.

Archive classification: math.FA math.SP

Mathematics Subject Classification: 47D03

The source file(s), ptwise_convergence_preprint.tex: 67741 bytes, is(are) stored in gzipped form as 0705.4510.gz with size 19kb. The corresponding postcript file has gzipped size 124kb.

Submitted from: r.taggart@unsw.edu.au

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