On the ε-entropy of classes of holomorphic functions

Suppose thatBRd is a ball of radiusR in ℂd and σ is the standard measure on the unit sphere in ℂd. ForR>1, 1≤p≤∞, and for the natural numbersl, d, byHR0(l, p, d) we denote the class of functionsf holomorphic inBRd and such that in the homogeneous polynomial expansion of the firstl summands the zero and radial derivatives of orderl belong to the closed unit ball of the Hardy spaceHp(BRd). In this paper an asymptotic formula for the ε-entropy of the classHR0(l, p, d) in the spacesLp(σ), 1≤p<∞, and\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$C(\bar B_1^d )$$ \end{document} is obtained.