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.
Digital Object Identifier (DOI)
"Calderon-Zygmund Operators and Singular Integrals,"
Applied Mathematics & Information Sciences: Vol. 15
, Article 13.
Available at: https://dc.naturalspublishing.com/amis/vol15/iss1/13