On some spaces of holomorphic functions of exponential growth on a half-plane
Marco M. Peloso, Maura Salvatori

TL;DR
This paper investigates generalized Hardy-Bergman spaces of holomorphic functions on a half-plane, analyzing their growth, structure, and relationships with classical spaces, including a Paley-Wiener theorem and kernel expressions.
Contribution
It introduces a new class of function spaces on the half-plane with specific growth conditions, providing a Paley-Wiener theorem, kernel formulas, and comparisons with classical spaces.
Findings
Spaces contain functions of order 1
Projection operator is unbounded for p≠2
Established a Paley-Wiener theorem for these spaces
Abstract
In this paper we study spaces of holomorphic functions on the right half-plane , that we denote by , whose growth conditions are given in terms of a translation invariant measure on the closed half-plane . Such a measure has the form , where is the Lebesgue measure on and is a regular Borel measure on . We call these spaces generalized Hardy-Bergman spaces on the half-plane . We study in particular the case of purely atomic, with point masses on an arithmetic progression on . We obtain a Paley-Wiener theorem for , and consequentely the expression for its reproducing kernel. We study the growth of functions in such space and in particular show that contains functions of order 1. Moreover, we prove that the orthogonal…
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