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

2019/05/12 by K. Kioulafa, Kioulafa, Kyranna
Mathematics · #Advanced Harmonic Analysis Research #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.1905.04676

openalex publication_date 2019/05/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we prove generic results concerning Hardy spaces in one or\nseveral complex variables. More precisely, we show that the generic function in\ncertain Hardy type spaces is totally unbounded and hence non-extentable,\ndespite the fact that these functions have non tangential limits at the\nboundary of the domain. We also consider local Hardy spaces and show that\ngenerically these functions do not belong, not even locally, to Hardy spaces of\nhigher order. We work first in the case of the unit ball of Cn where the\ncalculations are easier and the results are somehow better, and then we extend\nthem to the case of strictly pseudoconvex domains.\n

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