This article is cited in 2 papers

From the integral estimates of functions to uniform and locally averaged

R. A. Baladai, B. N. Khabibullin

Bashkir State University, 32 Z. Validi str., Ufa, 450076 Russia

Abstract: Problems of pointwise estimates from above of a function or its averages often arise in the function theory under known integral restrictions on the growth of this function. We offer an approach to such problems based on the integral Jensen inequality with the convex function.

Keywords: holomorphic function, average value, convex function, (pluri-)subharmonic function, $\overline\partial$-problem, integral Jensen's inequality, measure space.

UDC: 517.552

Received: 16.05.2016

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2017, 61:10, 11–20

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