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 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.
