By introducing independent parameters and applying the weight coefficients, we give an extended Hardy-Hilbert's inequality in the whole plane with a best possible constant factor. Furthermore, the equivalent forms, a… Click to show full abstract
By introducing independent parameters and applying the weight coefficients, we give an extended Hardy-Hilbert's inequality in the whole plane with a best possible constant factor. Furthermore, the equivalent forms, a few particular cases and the operator expressions are considered.
               
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