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

• Autorzy: Marco M. Peloso , Maura Salvatori
• 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.

Słowa kluczowe

EN

Holomorphic function on half-plane; Reproducing kernel Hilbert space; Hardy spaces, Bergman spaces

• Wydawca: De Gruyter Open
• Czasopismo: Concrete Operators
• Rocznik: 2016
• Tom: 3
• Numer: 1
• Strony: 52-67

Daty

otrzymano

2015-11-09

zaakceptowano

2016-04-05

online

2016-04-25

Twórcy

autor

Marco M. Peloso

• Dipartimento di Matematica, Università degli Studi di Milano, Via C. Saldini 50, 20133 Milano, Italy

autor

Maura Salvatori

• Dipartimento di Matematica, Università degli Studi di Milano, Via C. Saldini 50, 20133 Milano, Italy

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Identyfikatory

DOI

10.1515/conop-2016-0008