Maximal theorems for contraction semigroups in vector-valued Lebesgue spaces

Speaker: 

Dr. Robert Taggart

Affiliation: 

UNSW

Date: 

Wed, 19/03/2008 - 11:00am

Venue: 

RC-4082

Abstract: 

In this talk, we consider the extension of some classical theorems for contraction semigroups to the vector-valued Lp spaces. In particular, we generalise the maximal ergodic theorem of Hopf-Dunford-Schwartz and a maximal theorem for symmetric diffusion semigroups due to Stein-Cowling. 

The tools used include subpositivity, three different functional calculi for generators of such semigroups and some deep results from harmonic analysis in the setting of UMD spaces. 

As an application, it is shown how these new generalisations imply the pointwise convergence of solutions to certain evolution equations.

School Seminar Series: