We present a result of 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 continuity is got by means of continuity, thanks to an abstract theorem of Krein. Then 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: and continuity from Hölder estimates. Rev. Mat. Iberoam. 26 (2010), no. 1, pp. 347–366DOI 10.4171/RMI/604