Calculations of Norms for Monotone Operators on Cones of Functions with Monotonicity Properties

Abstract: The paper is devoted to the problem of exact calculation of the norms in ideal spaces for monotone operators on the cones of functions with monotonicity properties. We implement a general approach to this problem that covers many concrete variants of monotone operators in ideal spaces and different monotonicity conditions for functions. As applications, we calculate the norms of some integral operators on the cones, associate norms over some cones in Lebesgue spaces, the norms of the dilation operator and embedding operators on weighted Lorentz spaces with general weights. Under some more general conditions, we present order sharp estimates for Hardy-type operators on the cones. © 2021, Pleiades Publishing, Ltd.

Publisher
Pleiades Publishing
Number of issue
5
Language
English
Pages
857-874
Status
Published
Volume
42
Year
2021
Organizations
  • 1 Peoples Friendship University of Russia (RUDN University), Moscow, 117198, Russian Federation
Keywords
associate norms; conditions for convexity and concavity of the norms and operators; cone of monotone functions; decreasing rearrangement; dilation operator; ideal spaces; monotone operator

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