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

José García Cuerva; José María Martell

Publicacions Matemàtiques (2000)

- Volume: 44, Issue: 2, page 613-640
- ISSN: 0214-1493

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topGarcía Cuerva, José, and Martell, José María. "Weighted inequalities and vector-valued Calderón-Zygmund operators on non-homogeneous spaces.." Publicacions Matemàtiques 44.2 (2000): 613-640. <http://eudml.org/doc/41411>.

@article{GarcíaCuerva2000,

abstract = {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.},

author = {García Cuerva, José, Martell, José María},

journal = {Publicacions Matemàtiques},

keywords = {Integral de Cauchy; Medidas de Borel; Operadores integrales; Análisis armónico; non-doubling measures; Calderón-Zygmund operators; vector-valued inequalities; weights; Cauchy integral},

language = {eng},

number = {2},

pages = {613-640},

title = {Weighted inequalities and vector-valued Calderón-Zygmund operators on non-homogeneous spaces.},

url = {http://eudml.org/doc/41411},

volume = {44},

year = {2000},

}

TY - JOUR

AU - García Cuerva, José

AU - Martell, José María

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

JO - Publicacions Matemàtiques

PY - 2000

VL - 44

IS - 2

SP - 613

EP - 640

AB - 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.

LA - eng

KW - Integral de Cauchy; Medidas de Borel; Operadores integrales; Análisis armónico; non-doubling measures; Calderón-Zygmund operators; vector-valued inequalities; weights; Cauchy integral

UR - http://eudml.org/doc/41411

ER -

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