A property of series of holomorphic homogeneous polynomials with Hadamard gaps

Publisher: Cambridge University Press

E-ISSN: 1755-1633|53|3|479-484

ISSN: 0004-9727

Source: Bulletin of the Australian Mathematical Society, Vol.53, Iss.3, 1996-06, pp. : 479-484

Disclaimer: Any content in publications that violate the sovereignty, the constitution or regulations of the PRC is not accepted or approved by CNPIEC.

Previous Menu Next

Abstract

Recently J. Miao proved that if is a holomorphic function with Hadamard gaps on the open unit disc D then f Xp if and only if f Bp if and only if if and if only if where Xp, Bp and denote respectively the class of holomorphic functions on D which satisfy |f′(z)|p(1 − |z|2)p − 1dxdy is a finite measure, a Carleson measure and a little Carleson measure on D. In this paper we give a higher-dimensional version of Miao's result.