Characterisations of Hardy growth spaces with doubling weights

E. Doubtsov

Characterisations of Hardy growth spaces with doubling weights

Authors

E. Doubtsov St. Petersburg Department of V.A.Steklov Mathematical Institute

Keywords:

Hardy growth space, doubling weight

Abstract

Given

$p$ > 0 and a weight

$w$ , the Hardy growth space

$H(p, w)$ consists of those holomorphic functions

$f$ on the unit disc for which the integral means

$M_p(f, r)$ are estimated by

$Cw(r)$ , 0 < r < 1. Assuming that

$p$ > 1 and

$w$ satisfies a doubling condition, we characterise

$H(p, w)$ in terms of associated Fourier blocks. As an application, extending a result by Bennett, Stegenga and Timoney, we compute the solid hull of

$H(p, w)$ for p

$\geq$ 2. DOI: 10.1017/S0004972714000161

Published

2014-08-03

Issue

Vol. 90 No. 2 (2014)

Section

Articles

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