For analytic functions f on the unit disc whose alpha-th power is a sum of two weighted Bergman kernel functions, the sharp norm inequality ||f||_{A^{2alpha}_alpha} <= ||f||_{H^2} holds for all alpha > 1.
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A Sharp Inequality of Hardy-Littlewood Type Via Derivatives
For analytic functions f on the unit disc whose alpha-th power is a sum of two weighted Bergman kernel functions, the sharp norm inequality ||f||_{A^{2alpha}_alpha} <= ||f||_{H^2} holds for all alpha > 1.