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2016 | 3 | 1 | 52-67
Tytuł artykułu

On some spaces of holomorphic functions of exponential growth on a half-plane

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Wydawca
Czasopismo
Rocznik
Tom
3
Numer
1
Strony
52-67
Opis fizyczny
Daty
otrzymano
2015-11-09
zaakceptowano
2016-04-05
online
2016-04-25
Twórcy
  • Dipartimento di Matematica, Università degli Studi di Milano, Via C. Saldini 50, 20133 Milano, Italy
  • Dipartimento di Matematica, Università degli Studi di Milano, Via C. Saldini 50, 20133 Milano, Italy
Bibliografia
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  • [14] Krantz, Steven G. and Peloso, Marco M. and Caterina Stoppato, Completeness on the worm domain and the Müntz–Szász problem for the Bergman space, preprint, 2015
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Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_1515_conop-2016-0008
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