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

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