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On an Area Inequality and Weighted Integrals of Analytic Functions
Authors:Stevo Stević
Institution:1. Stevo Stevi?: Matemati?ki Fakultet, Studentski Trg 16, 11000 Beograd, Serbia, Yugoslavia
Abstract:In this note we investigate the relationship between the following integrals: $$\int_{U}\mid f^{(n)}(z)\mid^{p}\mid f^{(k)}(z)\mid^{q}(1-\mid z\mid )^{np+kq+\alpha}dm\ \ \ {\rm and}\ \ \ \int_{U}\mid f^{\prime}\mid^{p+q}(1-\mid z\mid)^{\alpha}dm$$ where 0 < p,q < ∞, α > ?1, k,n ∈ N ∪{0} and where ? is an arbitrary analytic function on the unit disc U.
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