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Some sufficient conditions for analytic functions to belong to \(\mathcal Q_{K,0}(p,q)\) space. (English) Zbl 1151.30321

Summary: 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 \(\lim_{|a|\to 1}\int_{\mathbb{D}}|f'(z)|^p(1-|z|^2)^q K(g(z,a))~dA(z)=0\).

MSC:

30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)
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