engleski

More accurate Hilbert-type inequalities in a difference form

In the present paper we establish several more accurate Hilbert-type inequalities in a difference form. Our main results rely on some recent improvements of the Young inequality. First, we give refinements and reverses of the H\"{; ; ; o}; ; ; lder inequality. Then, by virtue of the improved H\"{; ; ; o}; ; ; lder inequality, we give two classes of refinements and reverses for general Hilbert-type inequalities. As an application, we give strengthened forms of the classical Hilbert and Hardy inequalities.

Hilbert inequality ; Hardy inequality ; Young inequality

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