Boundedness of one class of integral operators from Lp to Lq for 1 < q< p< ∞


Oinarov R. Temirkhanova A. Kalybay A.
July 2023Birkhauser

Annals of Functional Analysis
2023#14Issue 3

In this paper, we obtain necessary and sufficient conditions for the boundedness of Volterra integral operators in Lebesgue spaces in the case 1 < q< p< ∞ . These operators belong to the classes O2± satisfying less restrictive conditions than the previously studied classes O1± , which we also discuss in the paper. For operators from the classes O1± we prove alternative boundedness criteria.

Boundedness , Integral inequality , Integral operator , Kernel , Weight function

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L.N. Gumilyov Eurasian National University, Satpaev Str. 2, Astana, 101008, Kazakhstan
KIMEP University, Abay Ave. 4, Almaty, 050010, Kazakhstan

L.N. Gumilyov Eurasian National University
KIMEP University

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