On Hardy type spaces in strictly pseudoconvex domains and the density, in these spaces, of certain classes of singular functions

Abstract

In this paper we prove generic results concerning Hardy spaces in one or several complex variables. More precisely, we show that the generic function in certain Hardy type spaces is totally unbounded and hence non-extentable, despite the fact that these functions have non tangential limits at the boundary of the domain. We also consider local Hardy spaces and show that generically these functions do not belong, not even locally, to Hardy spaces of higher order. We work first in the case of the unit ball of Cn where the calculations are easier and the results are somehow better, and then we extend them to the case of strictly pseudoconvex domains.