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Extension of Hilbert’s inequality
Mario Krni´c a,∗, Josip Peˇcari´c b
a Department of Mathematics, University of Zagreb, Bijeniˇcka cesta 30, 10000 Zagreb, Croatia
b Faculty of Textile Technology, University of Zagreb, Pierottijeva 6, 10000 Zagreb, Croatia
Received 25 May 2005
Available online 5 January 2006
Submitted by D. Waterman

Abstract
In this paper we make some further extensions of discrete Hilbert’s inequality by using Euler–Maclaurin
summation formula. We give the improvements of some previously obtained results and also compare our
results with some previously known from the literature.

1. Introduction
Hilbert’s and Hardy–Hilbert’s type inequalities are very significant weighted inequalities
which play an important role in many fields of mathematics. Similar inequalities, in operator
form, appear in harmonic analysis where one investigate properties of li