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Uspekhi Mat. Nauk, 2013, Volume 68, Issue 4(412), Pages 3–68 (Mi umn9538)  

This article is cited in 51 scientific papers (total in 51 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

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


DOI: https://doi.org/10.4213/rm9538

Full text: PDF file (1003 kB)
References: PDF file   HTML file

English version:
Russian Mathematical Surveys, 2013, 68:4, 597–664

Bibliographic databases:

UDC: 517.51
MSC: Primary 26D15; Secondary 47G10
Received: 02.02.2013

Citation: A. Gogatishvili, V. D. Stepanov, “Reduction theorems for weighted integral inequalities on the cone of monotone functions”, Uspekhi Mat. Nauk, 68:4(412) (2013), 3–68; Russian Math. Surveys, 68:4 (2013), 597–664

Citation in format AMSBIB
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    17. V. S. Guliyev, K. Koca, R. Ch. Mustafayev, T. Ünver, “Some operators arising from Schwarz BVP in complementary local Morrey-type spaces on the unit disc”, J. Math. Anal., 8:1 (2017), 130–142  mathscinet  isi
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