Some Sufficient Conditions for Analytic Functions to Belong to 𝒬 K , 0 ( p , q ) Space

Abstract

This paper gives some sufficient conditions for an analytic function to belong to the space consisting of all analytic functions $f$ on the unit disk such ${\lim }_{\left|a\right|\to 1}{\int }_{\hspace{0.17em}D}^{}{|f^{\prime }(z)|}^p{(1-{\left|z\right|}^2)}^{q}K\left(g\left(z,a\right)\right)dA\left(z\right)=0.$