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 belongnot even locallyto Hardy spaces of higher order. We work first in the case of the unit ball of n C where the calculations are easier and the results are somehow better, and then we extend them to the case of strictly pseudoconvex domains. ) (B which are totally unbounded in B is dense and  G in this space.

A project about chains of spaces, regarding topological and algebraic genericity and spaceability

“…These results are in the frame of the project presented in Section 4. A result complementing Theorem 8 is the following (see also [5] and [6]).…”

Generic versions of a result in the theory of Hardy spaces

“…We close this section mentioning that a complex function defined on the open unit disc D of C is called totally unbounded ( [9], [10], [5], [7]) if it is unbounded on D ∩ D(ζ 0 , r) for every r > 0 and…”