In this paper we explore conditions on variable symbols with respect to Haar systems,defining Calderón–Zygmund type operators with respect to the dyadic metrics associated to the Haar bases. We show that Petermi...In this paper we explore conditions on variable symbols with respect to Haar systems,defining Calderón–Zygmund type operators with respect to the dyadic metrics associated to the Haar bases. We show that Petermichl’s dyadic kernel can be seen as a variable kernel singular integral and we extend it to dyadic systems built on spaces of homogeneous type.展开更多
In this note we show that the general theory of vector valued singular integral operators of Calderón-Zygmund defined on general metric measure spaces,can be applied to obtain Sobolev type regularity properties f...In this note we show that the general theory of vector valued singular integral operators of Calderón-Zygmund defined on general metric measure spaces,can be applied to obtain Sobolev type regularity properties for solutions of the dyadic fractional Laplacian.In doing so,we define partial derivatives in terms of Haar multipliers and dyadic homogeneous singular integral operators.展开更多
基金Supported by Consejo Nacional de Investigaciones Científicas y Técnicas,Universidad Nacional del Litoral and Universidad Nacional del Comahue,Argentina
文摘In this paper we explore conditions on variable symbols with respect to Haar systems,defining Calderón–Zygmund type operators with respect to the dyadic metrics associated to the Haar bases. We show that Petermichl’s dyadic kernel can be seen as a variable kernel singular integral and we extend it to dyadic systems built on spaces of homogeneous type.
基金supported by the MINCYT in Argentina:CONICET and ANPCyT,UNL and UNComa。
文摘In this note we show that the general theory of vector valued singular integral operators of Calderón-Zygmund defined on general metric measure spaces,can be applied to obtain Sobolev type regularity properties for solutions of the dyadic fractional Laplacian.In doing so,we define partial derivatives in terms of Haar multipliers and dyadic homogeneous singular integral operators.
