On the Norm of a Multidimensional Hilbert-Type Operator
DOI:
https://doi.org/10.5644/SJM.07.2.08Keywords:
Hilbert-type inequality, Hardy-Hilbert type inequality, multidimensional Hilbert-type operator, homogeneous kernel, weight function, Beta function, Gamma function, normAbstract
In this paper we consider multidimensional Hilbert-type integral inequalities with non-conjugate exponents and homogeneous kernels of negative degree. As an application, we define related Hilbert-type integral operators and consider their norms. The problem of determining the norm of such operators is equivalent to the problem of the best possible constant factors involved in the right-hand sides of related inequalities. In such a way, we obtain the norms and the best possible constant factors in some general settings with conjugate exponents. In particular, we obtain generalizations of some recent results from the literature.
2000 Mathematics Subject Classification. Primary 47A07, 26D15
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