Calderon-Zygmund Operators and Singular Integrals

Authors

Mykola Yaremenko, National Technical University of Ukraine ”Igor Sikorsky Kyiv Polytechnic Institute” Kyiv, UkraineFollow

Author Country (or Countries)

Ukraine

Abstract

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)

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

Recommended Citation

Yaremenko, Mykola (2021) "Calderon-Zygmund Operators and Singular Integrals," Applied Mathematics & Information Sciences: Vol. 15: Iss. 1, Article 12.
DOI: http://dx.doi.org/10.18576/amis/150112
Available at: https://digitalcommons.aaru.edu.jo/amis/vol15/iss1/12