Boundedness Of Non-convolution Composition Operator On Weighted Carleson Measure Space

Suppose S1 and S2 are convolution Calderón-Zygmund operators with non-isotropic different homogeneities,then the boundedness of the composite operators S1 ○ S2 with mixed homogeneities on the weighted Carleson measure space and the weighted Hardy space depends on the commutability of the convolution operators.In this dissertation,we prove the boundedness of the composition operators T1 ○ T2 with mixed homogeneities on the weighted Carleson measure space,where T1 and T2 are non-convolution Calderón-Zygmund operators with non-isotropic different homogeneities.The non-commutability of non-convolution operators is overcome by Calderón reproducing formula and almost orthogonal estimate in Littlewood-Paley theory,and combining the annuli decomposition of the set of acceptable rectangles to proves that T1 ○ T2 is bounded on the weighted Carleson measure space.