Abstract of a paper by Robert J Taggart
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 The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0705.4510 or http://arXiv.org/abs/0705.4510 or by email in unzipped form by transmitting an empty message with subject line uget 0705.4510 or in gzipped form by using subject line get 0705.4510 to: math@arXiv.org.
participants (1)
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Dale Alspach