论文标题
Schatten班级和换向器在两个重量设置中，I。Hilbert Transform
Schatten classes and commutator in the two weight setting, I. Hilbert transform
论文作者
论文摘要
我们表征了希尔伯特（Hilbert）的换向器的希尔伯特（Hilbert）班级成员，在两个重量设置中。表征取决于换向器在新加权的贝托夫空间中的符号。这是从schatten类$ s_p $的结果中出现的，其中二元阶段性$ 1 <p <\ infty $。我们讨论将二元结果扩展到希尔伯特转型的全范围的Schatten类别的困难。
We characterize the Hilbert--Schmidt class membership of commutator with the Hilbert transform in the two weight setting. The characterization depends upon the symbol of the commutator being in a new weighted Besov space. This follows from a Schatten class $S_p$ result for dyadic paraproducts, where $1< p < \infty $. We discuss the difficulties in extending the dyadic result to the full range of Schatten classes for the Hilbert transform.
