JournalsrmiVol. 26, No. 1pp. 347–366

Singular integrals in nonhomogeneous spaces: L2L^2 and LpL^p continuity from Hölder estimates

  • Marco Bramanti

    Politecnico di Milano, Italy
Singular integrals in nonhomogeneous spaces: $L^2$ and $L^p$ continuity from Hölder estimates cover
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Abstract

We present a result of LpL^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 L2L^2 continuity is got by means of CαC^{\alpha} continuity, thanks to an abstract theorem of Krein. Then LpL^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: L2L^2 and LpL^p continuity from Hölder estimates. Rev. Mat. Iberoam. 26 (2010), no. 1, pp. 347–366

DOI 10.4171/RMI/604