RD空间上广义乘积Calderón-Zygmund算子在端点函数空间上的T1定理

The T1 theorem for the generalized product Calderón-Zygmund operator on product endpoint function spaces over RD spaces

在测度满足双倍条件与逆双倍条件、拟度量满足Holder正则性的乘积RD空间上,本文建立乘积Lipschitz端点函数空间的Littlewood-Paley特征刻画以及弱稠密性质,并证明了广义乘积Calderón-Zygmund算子在此端点函数空间上有界的充分必要条件是T1(1)=T2(1)=0.

The Littlewood-Paley characterization of the product Lipschitz endpoint function spaces and the density argument in the weak sense are established on product RD spaces,where the measures satisfy the doubling condition and the reverse doubling condition,and the quasi-metric satisfies the Holder regularity.Furthermore,we get the necessary and sufficient condition T1(1)=T2(1)=0 for the generalized product Calderón-Zygmund operator on product Lipschitz spaces.