A Hilbert-type inequality with a discrete fractional kernel
By introducing several positive parameters,a new fractional discrete kernel function is con-structed.By means of the method of weight coefficients,a double Hilbert series inequality is established,and the constant factor of the newly obtained inequality is proved to be the best possible.Furthermore,based on the rational fraction expansion of the cosecant function,it is also proved that the optimal constant factor can be represented by the cosecant function.At last,by assigning some specific values to the param-eters,some previously known results are obtained,and some new Hilbert-type inequalities with special kernel functions are also presented at the end of the paper.
Hilbert-type inequalityfractional kernel functionrational fraction expansioncosecant function
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