In this paper we study spaces of holomorphic functions on the right half-plane R, that we denote by Mpω, whose growth conditions are given in terms of a translation invariant measure ω on the closed half-plane R. Such a measure has the form ω = ν ⊗ m, where m is the Lebesgue measure on R and ν is a regular Borel measure on [0, +∞). We call these spaces generalized Hardy–Bergman spaces on the half-plane R. We study in particular the case of ν purely atomic, with point masses on an arithmetic progression on [0, +∞). We obtain a Paley–Wiener theorem for M2ω, and consequentely the expression for its reproducing kernel. We study the growth of functions in such space and in particular show that Mpω contains functions of order 1. Moreover, we prove that the orthogonal projection from Lp(R,dω) into Mpω is unbounded for p ≠ 2. Furthermore, we compare the spaces Mpω with the classical Hardy and Bergman spaces, and some other Hardy– Bergman-type spaces introduced more recently.
On some spaces of holomorphic functions of exponential growth on a half-plane / M.M. Peloso, M. Salvatori. - In: CONCRETE OPERATORS. - ISSN 2299-3282. - 3:1(2016 Apr), pp. 52-67.
|Titolo:||On some spaces of holomorphic functions of exponential growth on a half-plane|
PELOSO, MARCO MARIA (Primo)
SALVATORI, MAURA ELISABETTA (Ultimo)
|Parole Chiave:||Holomorphic function on half-plane; Reproducing kernel Hilbert space; Hardy spaces, Bergman spaces|
|Settore Scientifico Disciplinare:||Settore MAT/05 - Analisi Matematica|
|Data di pubblicazione:||apr-2016|
|Digital Object Identifier (DOI):||http://dx.doi.org/10.1515/conop-2016-0008|
|Appare nelle tipologie:||01 - Articolo su periodico|