ON FINITE AND INFINITE DECOMPOSITION OF SOME HILBERT'S TYPE INEQUALITIES

Alireza Moazzen

Abstract


In this work, some Hardy-Hilbert's integral inequalities with the best possible constants is proved. Also, some finite and infinite decompositions of sometype Hardy-Hilbert's integral operators is given. Indeed, for a non-negative kernel K, two Kernels K1 and K2 is given such that TK = TK1 + TK2 and ∥TK∥ =∥TK1∥ + ∥TK2∥. So, the space of bounded linear operators is strictly convex.Also, as an application of infinite decomposition of some Hardy-Hilbert's integraloperators, the convergence of some series of hypergeometric functions is given.

Keywords


Hilbert's inequality; innite decomposition; Hardy-Hilbert's integral operator; hypergeometric function.

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