一类具有可转移变量核的Hilbert型奇异重积分算子的有界性与范数及其应用

On the Boundedness and Norm of a Hilbert Type Singular Multiple Integral Operator with the Transferable Variable Kernel

研究Hilbert型奇异积分算子的重要问题之一,是讨论其积分核具有何种特征时算子是有界的,并进一步讨论算子的范数表达式.本文定义了含有两个参数的可转移变量函数,一般地,这是一种非齐次函数.本文利用权系数方法及实分析技巧,讨论了此类函数作为积分核的Hilbert型重奇异积分算子的有界性,得到其范数表达式及相应的参数条件,所得结果包含了诸多文献中的结论.最后,文中讨论了理论结果的应用.

One of important research issues about Hilbert-type singular integral operator is to discuss what characteristics the integral kernel should have so that the operator is bounded,and then to further examine the operator＇s norm expressions.In this paper,we introduce the concept of transferable variable functions with two parameters,in general,this is a nonhomogeneous function.Using weighting function methods and techniques of real analysis,we discuss the boundedness of the operator with such functions as the integral kernel,and obtain the norm expression of the operator and the corresponding parameters condition.These results extend many conclusions in other papers.Finally,we discuss the application of the obtained theoretical results.