L. S. Arendarenko, R. Oinarov, L.-E. Persson, “On the boundedness of some classes of integral operators in weighted Lebesgue spaces”, Eurasian Math. J., 2012, Volume 3, Number 1,Pages <nobr>5

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On the boundedness of some classes of integral operators in weighted Lebesgue spaces

L. S. Arendarenko^a, R. Oinarov^a, L.-E. Persson^b

^a Department of Fundamental and Applying Mathematics, Faculty of Mechanics and Mathematics, Eurasian National University, Astana, Kazakhstan
^b Department of Engineering Sciences and Mathematics Luleå University of Technology, SE-971 87 Luleå, Sweden

Abstract: Some new Hardy-type inequalities for Hardy-Volterra integral operators are proved and discussed. The case $1<q<p<\infty$ is considered and the involved kernels satisfy conditions, which are less restrictive than the usual Oinarov condition.

Keywords and phrases: Hardy type inequalities, boundedness, integral operators, kernels, weighted Lebesgue spaces.

MSC: 47G10, 47B38

Received: 06.09.2011

Language: English