In this article, we establish conditions on continuous restrictively bounded linear mapping T from S to S′ associated with the kernel K under which the operator T extends to a bounded operator T : Lp Rl → Lp Rl. Next, we generalize the interpolation theorem 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 inequality M ̃ 1 −1 M ̃ 1 (|T ( f )|)μ ≤ A1 M ̃ 1 −1 M ̃ 1 (| f |)μ holds for the constant A1 that depends only on A, M1, M2.
Digital Object Identifier (DOI)
"Calderon-Zygmund Operators and Singular Integrals,"
Applied Mathematics & Information Sciences: Vol. 15:
1, Article 12.
Available at: https://digitalcommons.aaru.edu.jo/amis/vol15/iss1/12