A GENERALIZATION OF A RESULT OF CHOA ON ANALYTIC FUNCTIONS WITH HADAMARD GAPS
A GENERALIZATION OF A RESULT OF CHOA ON ANALYTIC FUNCTIONS WITH HADAMARD GAPS
In this paper we obtain a sufficient and necessary condition for an analytic function f on the unit ball B with Hadamard gaps, that is, for <TEX>$f(z)\;=\;{\sum}^{\infty}_{k=1}\;P_{nk}(z)$</TEX> (the homogeneous polynomial expansion of f) satisfying <TEX>$n_{k+1}/n_{k}{\ge}{\lambda}>1$</TEX> for all <TEX>$k\;{\in}\;N$</TEX>, to belong to the weighted Bergman space <TEX>$$A^p_{\alpha}(B)\;=\;\{f{\mid}{\int}_{B}{\mid}f(z){\mid}^{p}(1-{\mid}z{\mid}^2)^{\alpha}dV(z) < {\infty},\;f{\in}H(B)\}$$</TEX>. We find …