一个联系指数函数中间变量的全平面Hilbert积分不等式

A full-planar Hilbert integral inequality related to middle-variable of exponential function

引入指数函数中间变量,应用权函数及实分析技巧,建立一个具有最佳常数因子的全平面Hilbert型积分不等式,考虑了其等价式、算子表示、特例及齐次形式.

By introducing middle-variable of exponential function and applying weight function and real analysis skill,a full-planar Hilbert-type integral inequality with optimal constant factor is established.Its equivalent formula,operator expressions,special case,and homogeneous form are taken into consideration,also.