Order-sharp estimates for decreasing rearrangements of convolutions

E. G. Bakhtigareeva^a, M. L. Goldman

^a Department of Function Theory, Steklov Mathematical Institute of the Russian Academy of Sciences, 8 Gubkin St, 119991 Moscow, Russian Federation

Abstract: In this paper, we study estimates for convolutions on some classes of measurable, positive and radial symmetrical functions. On this base we prove then order-sharp estimates for decreasing and symmetrical rearrangements of convolutions and for weighted mean values of rearrangements. These estimates give, in particular, a reversal of the well-known inequalities for convolutions proved by R. O’Neil.

Keywords and phrases: convolutions, radial symmetrical functions, order-sharp estimates, decreasing rearrangements, symmetrical rearrangements, mean values of rearrangements.

MSC: 46E30, 47A15, 47A30

Received: 03.06.2024

Language: English

DOI: 10.32523/2077-9879-2024-15-4-08-32

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