Weighted inequalities and vector-valued Calderón-Zygmund operators on non-homogeneous spaces.

Título inglés Weighted inequalities and vector-valued Calderón-Zygmund operators on non-homogeneous spaces.
Título español Desigualdades ponderadas y operadores Calderón-Zygmund valuados vectoriales sobre espacios no homogéneos.
Autor/es García Cuerva, José ; Martell, José María
Organización Dep. Mat. Univ. Autón. Madrid, Madrid, España
Revista 0214-1493
Publicación 2000, 44 (2): 613-640, 24 Ref.
Tipo de documento articulo
Idioma Inglés
Resumen inglés Recently, F. Nazarov, S. Treil and A. Volberg (and independently X. Tolsa) have extended the classical theory of Calderón-Zygmund operators to the context of a non-homogeneous space (X,d,μ) where, in particular, the measure μ may be non-doubling. In the present work we study weighted inequalities for these operators. Specifically, for 1 < p < ∞, we identify sufficient conditions for the weight on one side, which guarantee the existence of another weight in the other side, so that the weighted Lp inequality holds. We deal with this problem by developing a vector-valued theory for Calderón-Zygmund operators on non-homogeneous spaces which is interesting in its own right. For the case of the Cauchy integral operator, which is the most important example, we even prove that the conditions for the weights are also necessary.
Clasificación UNESCO 120213
Palabras clave español Integral de Cauchy ; Medidas de Borel ; Operadores integrales ; Análisis armónico
Código MathReviews MR1800824
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