engleski

On Hilbert type inequalities

In this talk we give some new generalizations of classical Hilbert's inequality. We extend it to a general case with $k\geq 2$ non-conjugate exponents. The established technique is then applied to the case where functions are defined $R^n$, and in the case of conjugate exponents and some special homogeneous kernels it is shown that the obtained inequalities are the best possible. A generalization of the Hilbert-Pachpatte inequality and refinements of the Hilbert inequality using the Laplace transform are also presented. The problem of the best possibility of the Hilbert inequality with a general homogeneous kernel is considered in the case where functions are defined on $R_{;+};$.

Hardy-Hilbert's inequality; homogeneous kernel; the best possible constant; conjugate exponents; non-conjugate exponents; the hypergeometric fuction

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