半平面上指数增长全纯函数的一些空间

IF 0.3 Q4 MATHEMATICS Concrete Operators Pub Date : 2015-12-03 DOI:10.1515/conop-2016-0008
M. Peloso, M. Salvatori
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引用次数: 11

摘要

摘要本文研究了右半平面R上的全纯函数空间,用m ω表示,其生长条件用闭半平面R上的平移不变测度ω给出,该测度的形式为ω = ν⊗m,其中m为R上的Lebesgue测度,ν为R上的正则Borel测度[0,+∞]。我们称这些空间为半平面r上的广义Hardy-Bergman空间。我们特别研究了ν纯原子的情况,其质点在&[0,+∞)上的等差数列上。我们得到了M2ω的一个Paley-Wiener定理,并由此得到了它的再现核的表达式。我们研究了函数在这个空间中的生长,特别地证明了m ω包含1阶的函数。进一步证明了Lp(R,dω)到Mpω的正交投影在p≠2时是无界的。此外,我们将空间Mpω与经典Hardy和Bergman空间以及最近引入的其他一些Hardy - Bergman型空间进行了比较。
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On some spaces of holomorphic functions of exponential growth on a half-plane
Abstract 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 Œ[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 Œ[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.
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来源期刊
Concrete Operators
Concrete Operators MATHEMATICS-
CiteScore
1.00
自引率
16.70%
发文量
10
审稿时长
22 weeks
期刊最新文献
On the compactness and the essential norm of operators defined by infinite tridiagonal matrices m-Isometric tensor products Estimation of coefficient bounds for a subclass of Sakaguchi kind functions mapped onto various domains Generalized Crofoot transform and applications Generalized Hausdorff operator on Bergmann spaces
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