Some inequalities of isoperimetric type concerning analytic and subharmonic functions

M. Mateljevi{\cj} and M. Pavlovi{\cj}

Abstract: We prove an inequality between the weighted Bergman and Hardy norm of an analytic function and generalize this to the ratio of two log-subharmonic function. These results may be regarded as a generalization of the classical isoperimetric inequality.

Keywords: Hardy and weighted Bergman spaces, the reproducing kernel, the Riesz decomposition of log-subharmonic function and the isoperimetric inequality

Classification (MSC2000): 30D55; 31B05, 30C40

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