On singular integrals of Calderón-type in Rn and BMO

• Autores: Steve Hofmann
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 10, Nº 3, 1994, págs. 467-506
• Idioma: inglés
• DOI: 10.4171/rmi/159
• Títulos paralelos:
  • Integrales singulares del tipo Calderón en Rn y BMO.
• Enlaces
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• Resumen

  • We prove Lp (and weighted Lp) bounds for singular integrals of the form p.v. ?Rn E (A(x) - A(y) / |x - y|) (O(x - y) / |x - y|n) f(y) dy, where E(t) = cos t if O is odd, and E(t) = sin t if O is even, and where Ñ A Î BMO. Even in the case that O is smooth, the theory of singular integrals with rough kernels plays a key role in the proof. By standard techniques, the trigonometric function E can then be replaced by a large class of smooth functions F. Some related operators are also considered. As a further application we prove a compactness result for certain layer potentials.