论文标题
cauchy单数积分运算符，带有log-hölder空间中的参数
Cauchy singular integral operator with parameters in Log-Hölder spaces
论文作者
论文摘要
本文是由Muskhelishvili古典教科书中的主张激励的，该教科书在Hölder函数上涉及Cauchy单数积分运算符$ s $。与索赔相反，Tumanov构建了一个反示例，该示例表明，具有参数的$ S $无法维持相同的Hölder规律性相对于参数。鉴于该示例，研究了cauchy单数积分运算符的行为，其中具有log-hölder空间之间的参数，以获得尖锐的规范估计。在论文的结尾，我们讨论了其在产品域上的$ \ bar \ partial $问题的应用。
This paper is motivated by a claim in the classical textbook of Muskhelishvili concerning the Cauchy singular integral operator $S$ on Hölder functions with parameters. To the contrary of the claim, a counter example was constructed by Tumanov which shows that $S$ with parameters fails to maintain the same Hölder regularity with respect to the parameters. In view of the example, the behavior of the Cauchy singular integral operator with parameters between a type of Log-Hölder spaces is investigated to obtain the sharp norm estimates. At the end of the paper, we discuss its application to the $\bar\partial$ problem on product domains.
