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Author Country (or Countries)

Ukraine

Abstract

In this article, we establish conditions on continuous restrictively bounded linear mapping T from S to S′ associated withthe kernel K under which the operator T extends to a bounded operator T: Lp(Rl) → Lp(Rl). Next, we generalize the interpolationtheorem for new functional classes, we show that bounded operator T defined, whose kernel satisfies the standard conditions, is bounded()()with respect to convex seminorm, so, an inequalityM1−1M1 (|T (f)|)≤A1M1−1M(| f |)µ1µ holdsfortheconstantA1 thatdepends only on A, M1, M2.

Suggested Reviewers

N/A

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/amis/150112

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