This article is cited in 2 papers

On a class of spaces of analytic functions

M. I. Gvaradze

Tbilisi State University

Abstract: The spaces $B(p,q,\lambda)$ ($0<p<q\le\infty$, $0<\lambda\le\infty$) of functions, analytic in the circle $|z|<1$, are introduced, and an unimprovable estimate is obtained for the Taylor coefficients of a function $f\in B(p,q,\lambda)$. It is shown that $B(p,q,\lambda)$ is the space of fractional derivatives $f^{(\alpha}$ of order $\alpha$ ($-\infty<\alpha<1/p-1/q$) of a function $f$ of $B(s,q,\lambda)$, where $s=p/(1-\alpha p)$.

UDC: 517

Received: 16.05.1974

 English version: Mathematical Notes, 1977, 21:2, 79–84

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