Revista Matemática Iberoamericana


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Volume 26, Issue 1, 2010, pp. 347–366
DOI: 10.4171/RMI/604

Published online: 2010-04-30

Singular integrals in nonhomogeneous spaces: $L^2$ and $L^p$ continuity from Hölder estimates

Marco Bramanti[1]

(1) Politecnico di Milano, Italy

We present a result of $L^p$ continuity of singular integrals of Calderón-Zygmund type in the context of bounded nonhomogeneous spaces, well suited to be applied to problems of a priori estimates for partial differential equations. First, an easy and selfcontained proof of $L^2$ continuity is got by means of $C^{\alpha}$ continuity, thanks to an abstract theorem of Krein. Then $L^p$ continuity is derived adapting known results by Nazarov-Treil-Volberg about singular integrals in nonhomogeneous spaces.

Keywords: Singular integrals, nonhomogeneous spaces, $L^p$ spaces, Hölder spaces

Bramanti Marco: Singular integrals in nonhomogeneous spaces: $L^2$ and $L^p$ continuity from Hölder estimates. Rev. Mat. Iberoamericana 26 (2010), 347-366. doi: 10.4171/RMI/604