On the Marcinkiewicz–Calderón Interpolation Theorem for Integral Operators
Nursultanov E.D. Tleukhanova N.T. Mukeeva Z.M.
April 2022Pleiades journals
Mathematical Notes
2022#111Issue 3-4423 - 432 pp.
Abstract: The inverse problem to the classical Marcinkiewicz–Calderón interpolation theorem is considered. Necessary conditions for the Marcinkiewicz–Calderón theorem to hold for the integral operator under consideration are obtained in terms of the kernel of this operator. It is shown that these conditions are sufficient for the given integral operator to be of (p,q)-strong type for the same parameters p and q that appear in the interpolation theorem.
integral operators , Marcinkiewicz interpolation theorem
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Kazakhstan Branch of Lomonosov Moscow State University, Nur-Sultan, 473021, Kazakhstan
Institute of Mathematics and Mathematical Modeling, Almaty, 050010, Kazakhstan
Gumilev Eurasian National University, Nur-Sultan, 010008, Kazakhstan
Kazakhstan Branch of Lomonosov Moscow State University
Institute of Mathematics and Mathematical Modeling
Gumilev Eurasian National University
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