Singular integrals in nonhomogeneous spaces: $L^2$ and $L^p$ continuity from Hölder estimates
Rev. Mat. Iberoamericana, Tome 26 (2010) no. 1, p. 347-366 / Harvested from Project Euclid
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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.
Publié le : 2010-03-15
Classification:  singular integrals,  nonhomogeneous spaces,  $L^p$ spaces,  Hölder spaces,  42B20,  47B38 
@article{1266330127,
     author = {Bramanti
, 
Marco},
     title = {Singular integrals in nonhomogeneous spaces: $L^2$ and $L^p$ continuity from H\"older estimates},
     journal = {Rev. Mat. Iberoamericana},
     volume = {26},
     number = {1},
     year = {2010},
     pages = { 347-366},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1266330127}
}

Bramanti
, 
Marco. Singular integrals in nonhomogeneous spaces: $L^2$ and $L^p$ continuity from Hölder estimates. Rev. Mat. Iberoamericana, Tome 26 (2010) no. 1, pp.  347-366. http://gdmltest.u-ga.fr/item/1266330127/