Vector valued Hardy spaces related to analytic functions having distributional boundary values

Abstract

© 2019, © 2019 Informa UK Limited, trading as Taylor & Francis Group. The Hardy space Hp of vector valued analytic functions in tube domains in Cn and with values in Banach space are defined. Analytic functions in tube domains in Cn with values in Hilbert space which have Lp functions with values in Hilbert space as distributional boundary value are proved to be in Hp. A Poisson integral representation for such vector valued analytic functions is obtained.