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Russian Mathematical Surveys, 2013, Volume 68, Issue 4, Pages 597–664
DOI: https://doi.org/10.1070/RM2013v068n04ABEH004849 (Mi rm9538) 		 
This article is cited in 66 scientific papers (total in 66 papers)

Reduction theorems for weighted integral inequalities on the cone of monotone functions

A. Gogatishvilia, V. D. Stepanovb

a Mathematical Institute, Academy of Sciences of the Czech Republic
b Peoples Friendship University of Russia
English version PDF (965 kB) Citations (66) Russian version article
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DOI: https://doi.org/10.1070/RM2013v068n04ABEH004849
Abstract: This paper surveys results related to the reduction of integral inequalities involving positive operators in weighted Lebesgue spaces on the real semi-axis and valid on the cone of monotone functions, to certain more easily manageable inequalities valid on the cone of non-negative functions. The case of monotone operators is new. As an application, a complete characterization for all possible integrability parameters is obtained for a number of Volterra operators.
Bibliography: 118 titles.
Keywords: weighted Lebesgue space, cone of monotone functions, duality principle, weighted integral inequality, bounded operators, reduction theorem.
Funding agency Grant number
Czech Science Foundation 201-08-0383
P201-13-14743S
Institute of Mathematics of the Academy of Sciences of the Czech Republic RVO: 67985840
Russian Foundation for Basic Research 12-01-00524
12-01-00554
Far Eastern Branch of the Russian Academy of Sciences 12-I-OMN-01
12-II-С0-01M-002
Received: 02.02.2013
Bibliographic databases:
Document Type: Article
UDC: 517.51
MSC: Primary 26D15; Secondary 47G10
Language: English
Original paper language: Russian
Citation: A. Gogatishvili, V. D. Stepanov, “Reduction theorems for weighted integral inequalities on the cone of monotone functions”, Russian Math. Surveys, 68:4 (2013), 597–664
Citation in format AMSBIB
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\by A.~Gogatishvili, V.~D.~Stepanov
\paper Reduction theorems for weighted integral inequalities on the cone of monotone functions
\jour Russian Math. Surveys
\yr 2013
\vol 68
\issue 4
\pages 597--664
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    • This publication is cited in the following 66 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    References:112
    First page:50
     
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