Abstract
By applying the method of weight functions and the technique of real analysis, a multidimensional Hilbert-type integral inequality with multi-parameters and the best possible constant factor related to the gamma function is given. The equivalent forms and the reverses are obtained. We also consider the operator expressions and a few particular results related to the kernels of non-homogeneous and homogeneous.
Highlights
Suppose that p > + q =, f (x), g(y) ≥ ∈ Lp(R+), g Lq(R+), f p=( ∞
>, b q >, we still have the discrete variant of the above inequality with the same best constant π sin(π /p) ambn < π m + n sin(π/p)
By using the transfer formula and applying the method of weight functions and the technique of real analysis, we give a multidimensional Hilbert-type integral inequality with multi-parameters and the best possible constant factor related to the gamma function
Summary
We have the following well-known Hardy-Hilbert integral inequality (cf [ ]):. Where the constant factor π sin(π /p) is best possible. > , b q > , we still have the discrete variant of the above inequality with the same best constant π sin(π /p) as follows: ambn < π m + n sin(π/p). Inequalities ( ) and ( ) are important in the analysis and its applications (cf [ – ]). In , by introducing an independent parameter λ ∈
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