论文标题
分数矢量riesz的两个重量Sobolev规范不平等变化和加倍重量
Two weight Sobolev norm inequalities for fractional vector Riesz transforms and doubling weights
论文作者
论文摘要
我们证明了分数矢量riesz的T1定理将映射一个加权的Sobolev空间映射到另一个映射，其中权重正在欧几里得空间上加倍措施。有界性的特征在于经典的A_2条件和两个立方体指标上的两个双重测试条件。我们还显示了各种加权Sobolev规范的等效性，当该度量加倍，这通常是失败的。
We prove a T1 theorem for fractional vector Riesz transforms mapping one weighted Sobolev space to another, where the weights are doubling measures on Euclidean space. Boundedness is characterized by the classical A_2 condition and two dual testing conditions on indicators of cubes. We also show the equivalence of various weighted Sobolev norms when the measure is doubling, something that fails in general.
