Weighted norm inequalities for Calderón-Zygmund operators without doubling conditions.

Título inglés Weighted norm inequalities for Calderón-Zygmund operators without doubling conditions.
Título español Desigualdades de norma ponderadas para operadores de Calderón-Zygmund sin condiciones doblantes.
Autor/es Tolsa, Xavier
Organización Inst. Catal. Rec. Estud. Avanc. (ICREA) Dep. Mat. Univ. Autòn. Barcelona, Barcelona, España
Revista 0214-1493
Publicación 2007, 51 (2): 397-456, 22 Ref.
Tipo de documento articulo
Idioma Inglés
Resumen inglés Let µ be a Borel measure on Rd which may be non doubling. The only condition that µ must satisfy is µ(B(x, r)) ≤ Crn for all x Î Rd, r > 0 and for some fixed n with 0 < n ≤ d. In this paper we introduce a maximal operator N, which coincides with the maximal Hardy-Littlewood operator if µ(B(x, r)) ≈ rn for x Î supp(µ), and we show that all n-dimensional Calderón-Zygmund operators are bounded on Lp(w dµ) if and only if N is bounded on Lp(w dµ), for a fixed p Î (1, ∞). Also, we prove that this happens if and only if some conditions of Sawyer type hold. We obtain analogous results about the weak (p,p) estimates. This type of weights do not satisfy a reverse Hölder inequality, in general, but some kind of self improving property still holds. On the other hand, if Î RBMO(µ) and ε > 0 is small enough, then eεf belongs to this class of weights.
Clasificación UNESCO 120213
Palabras clave español Integrales singulares ; Operadores de Calderón-Zygmund ; Operador maximal de Hardy-Littlewood ; Desigualdades
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