Sufficiently necessary conditions for the optimal matching parameters of super-homogeneous kernel integral operator in Lebesgue space with added exponential weight(加指数权Lebesgue空间超齐次核积分算子搭配参数最佳的充要条件)

Abstract

The concept of super-homogeneous function is introduced, the homogeneous kernel, quasi-homogeneous kernel and many non-homogeneous kernel are united as super-homogeneous, as well as the boundedness problems of super-homogeneous kernel integral operator are discussed in the Lebesgue space of the added exponential weight, the sufficiently necessary conditions for the best matching parameters of bounded operators are obtained, and the problem of calculating the operator norm is solved. Finally some special cases are given as applications.(引入超齐次函数概念，将齐次核、拟齐次核和若干非齐次核统一为超齐次核。利用权系数方法，讨论了加指数权Lebesgue空间超齐次核积分算子的有界性与算子范数问题，得到了有界算子搭配参数最佳的充分必要条件，解决了算子范数的计算问题，并给出了一些应用特例。)

Keywords

• super-homogeneous function(超齐次核)
• integral operator(积分算子)
• hilbert-type integral inequality(hilbert型积分不等式)
• lebesgue space with added exponential weight(加指数权lebesgue空间)
• the optimal matching parameter(最佳搭配参数)
• bounded operator(有界算子)
• operator norm(算子范数)