Skip to main content
Article thumbnail
Location of Repository

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

By Gordon Blower, Ian Doust and Robert Taggart

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

Publisher: Australian National University
Year: 2010
OAI identifier: oai:eprints.lancs.ac.uk:28029
Provided by: Lancaster E-Prints

Suggested articles

Citations

  1. (2005). A maximal theorem for holomorphic semigroups, doi
  2. (1996). Banach space operators with a bounded H∞ functional calculus, doi
  3. (1979). Equations of evolution,
  4. (1983). Harmonic analysis on semigroups, doi
  5. (1975). Methods of modern mathematical physics II: Fourier analysis and self-adjointness, doi
  6. (1980). One-parameter semigroups, doi
  7. (2009). Pointwise convergence for semigroups in vector-valued Lp spaces, doi
  8. (1970). Topics in harmonic analysis related to the Littlewood–Paley theory,
  9. (1977). Vector Measures,

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.