一个新的实齐次核的Hilbert型积分不等式及其等价形式

摘要

通过引入双参数的实齐次核,应用权函数方法给出一个新的有最佳常数因子的Hilbert型积分不等式及其等价形式,并证明了常数因子的最佳性,它与ψ函数有关.同时,给出了逆向不等式及相应的等价形式.%Having introduced a homogeneous kernel of real number-degree with two independent parameters and estimating the weight function, we gave a new Hilbert-type integral inequality with a real number-degree with a best constant factor, it involves the equivalent inequality with reverse forms considered. It involves the ψ function. The reverse inequality and their corresponding equivalent forms were given.