奇异算子Q-变差在齐型空间上的最优加权估计

SHARP WEIGHTED ESTIMATES FOR Q-VARIATIONS OF SINGULAR OPERATORS ON THE SPACES OF HOMOGENEOUS TYPE

我们将齐型空间上的Ap理论的最优权有界性推广到了平均算子和Calderon–Zygmund算子的q变差.这些结果利用了Lorist和Omisboand在齐型空间上给出的新的稀疏控制技术[1]以及[2].最后我们还讨论了这些理论的应用.

In this work we extend the theorems of the sharp A p weights to the q-variation of average operators and Calder´on–Zygmund operators on the spaces of homogeneous type.These results make use of the new sparse dominating techniques given by Lerner and Omisboand on Eu-clidean spaces[1],and Lorist[2]in the setting of homogeneous spaces.In particular,we establish the sparse pointwise estimates for the parabolic operators.At last,we also discuss some applications of our theorems.