On the geometric mean operator with variable limits of integration

DOI10.1134/S0081543808010185zbMath1233.42001MaRDI QIDQ666561

Elena P. Ushakova, Vladimir D. Stepanov

Publication date: 8 March 2012

Published in: Proceedings of the Steklov Institute of Mathematics (Search for Journal in Brave)

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Linear operators on function spaces (general) (47B38)

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On weighted Sobolev spaces on the real line ⋮ Hardy-Steklov operators and Sobolev-type embedding inequalities ⋮ Hardy-Steklov integral operators. II ⋮ Characterization of the function spaces associated with weighted Sobolev spaces of the first order on the real line ⋮ On the boundedness and compactness of a certain integral operator ⋮ Операторы Харди - Стеклова и принцип двойственности в весовых пространствах Соболева первого порядка на действительной оси ⋮ Boundedness criteria for the Hardy-Steklov operator expressed in terms of a fairway function ⋮ Hardy-Steklov integral operators. I ⋮ BOUNDEDNESS AND COMPACTNESS OF A CERTAIN CLASS OF MATRIX OPERATORS WITH VARIABLE LIMITS OF SUMMATION ⋮ Integral operators with two variable integration limits on the cone of monotone functions ⋮ Reduction theorems for weighted integral inequalities on the cone of monotone functions ⋮ A duality principle in weighted Sobolev spaces on the real line

Cites Work

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• The generalized Hardy operator with kernel and variable integral limits in Banach function spaces
• Generalized Hardy operators and normalizing measures.
• Weighted integral inequalities with the geometric mean operator
• Hardy operator with variable limits on monotone functions
• The Weighted Hardy Inequality: New Proofs and the Case p = 1

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