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March, 2010 Singular integrals in nonhomogeneous spaces: $L^2$ and $L^p$ continuity from Hölder estimates
Marco Bramanti
Rev. Mat. Iberoamericana 26(1): 347-366 (March, 2010).


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.


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Marco Bramanti . "Singular integrals in nonhomogeneous spaces: $L^2$ and $L^p$ continuity from Hölder estimates." Rev. Mat. Iberoamericana 26 (1) 347 - 366, March, 2010.


Published: March, 2010
First available in Project Euclid: 16 February 2010

zbMATH: 1205.42011
MathSciNet: MR2666318

Primary: 42B20
Secondary: 47B38

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

Rights: Copyright © 2010 Departamento de Matemáticas, Universidad Autónoma de Madrid

Vol.26 • No. 1 • March, 2010
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