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Recently, V. Cruz, J. Mateu and J. Orobitg have proved a T(1) theorem for the Beurling transform in the complex plane. It asserts that given 0 < s 1, 1 p ∞ with sp 2 and a Lipschitz domain Ω ⊂ C, the Beurling transform Bf = −p.v. 1 πz2 ∗ f is bounded in the Sobolev space Ws,p(Ω) if and only if BχΩ ∈ Ws,p(Ω). In this paper we obtain a generalized version of the former result valid for any s ∈ N and for a larger family of Calderón–Zygmund operators in any ambient space Rd as long as p d. In that case we need to check the boundedness not only over the characteristic function of the domain, but over a finite collection of polynomials restricted to the domain. Finally wefind a sufficient condition in terms of Carleson measures for p d. In the particular case s = 1, this condition is in fact necessary, which yields a complete characterization.
Idioma original | Anglès |
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Pàgines (de-a) | 2946-2989 |
Nombre de pàgines | 44 |
Revista | Journal of Functional Analysis |
Volum | 268 |
Número | 10 |
DOIs | |
Estat de la publicació | Publicada - 1 de gen. 2015 |
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Navegar pels temes de recerca de 'A T(P) theorem for Sobolev spaces on domains'. Junts formen un fingerprint únic.Projectes
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Integrales singulares, teoría geométrica de la medida, y espacios de Sobolev
Tolsa Domenech, X. (PI), Conde Alonso, J. M. (Col.laborador/a), Melnikov Fishkina, M. (Col.laborador/a), Reguera Rodríguez, M. D. C. (Col.laborador/a), Uriarte-Tuero, I. (Col.laborador/a), Martin Pedret, J. (Investigador/a) & Prat Baiget, L. (Investigador/a)
Ministerio de Economía y Competitividad (MINECO)
1/01/14 → 31/12/16
Projecte: Projectes i Ajuts a la Recerca