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A maximal theorem for holomorphic semigroups on vector-valued spaces.

Research output: Contribution in Book/Report/ProceedingsChapter

Published

Publication date2010
Host publicationThe AMSI-ANU Workshop on Spectral Theory and Harmonic Analysis : The Australian National University, Canberra, July 2009
EditorsAndrew Hassell, Alan McIntosh, Robert Taggart
Place of publicationCanberra
PublisherAustralian National University
Pages105-114
Number of pages10
Volume44
Edition44
ISBN (Print)0 7315 5208 3
Original languageEnglish

Publication series

NameProceedings of the Centre for Mathematics and its Applications
PublisherAustralian National University

Abstract

Suppose that 1<p\leq \infty (\Omega ,\mu) is a \sigma finite measure space and E is a closed subspace of Labesgue Bochner space L^p(\Omega; E) consisting of function oon \Omega that take their values in some complex Banach space X. Suppose that -A is invertible and generates a bounded hlomorphic semigroup T_z on E. If 0<\alpha <1, and f belongs to the domain of A^\alpha, then the maximal function \sup_z|T_zf|, where the supremum is taken over any sector contained in the sector of holomorphy, belongs to L^p. This extends an earlier result of Blower and Doust.