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

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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.

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