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

  • Marco Bramanti

    Politecnico di Milano, Italy

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.

Cite this article

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