Growth properties and sequences of zeros of analytic functions in spaces of Dirichlet type

Journal of the Australian Mathematical Society

Daniel Girela¹ 

[1] José Ángel Peláez

关键词: primary 30D35;    30D55;    46E15;   

DOI  :  10.1017/S1446788700014105

学科分类：数学（综合）

来源: Cambridge University Press

【 摘 要 】

For 0 < p < ∞, we let pp−1 denote the space of those functions f that are analytic in the unit disc Δ = {z ∈ C: |z| < 1} and satisfy ∫Δ(1 – |z|)p−1|f′(z)|pdx dy < ∞ The spaces pp−1 are closely related to Hardy spaces. We have, p−1p ⊂ Hp, if 0 < p ≦ 2, and Hp ⊂ pp−1, if 2 ≦ p < ∞. In this paper we obtain a number of results about the Taylor coefficients of pp-1 -functions and sharp estimates on the growth of the integral means and the radial growth of these functions as well as information on their zero sets.2000 Mathematics subject classification: primary 30D35, 30D55, 46E15.

【 授权许可】

Unknown