POINTWISE CONVERGENCE AND SEMIGROUPS ACTING ON VECTOR-VALUED FUNCTIONS

Authors

  • Michael G Cowling
  • Michael Leinert

Abstract

A submarkovian C0 semigroup (Tt)t2R+ acting on the scale of complex-valued functions Lp(X;C) extends to a semigroup of operators on the scale of vector-valued function spaces Lp(X;E), when E is a Banach space. It is known that, if f 2 Lp(X;C), where 1 < p < 1, then Ttf ! f pointwise almost everywhere. We show that the same holds when f 2 Lp(X;E)

Published

2011-10-19

Issue

Vol. 84 No. 1 (2011)

Section

Articles
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