| where the constant factor π is the best possible. There are also some inequalitiessimilar to Hilbert’s inequality, which are known as Hilbert-type inequalities. These inequal-ities are important and there are many applications in mathematical analysis. Considerableattention has recently been given to these inequalities by many authors and many new andinteresting results have been obtained. In this paper, we further study this type inequali-ties. We study certain linear series operators, prove the boundedness of these operators onweighted series spaces lwpand obtain the sharp norm estimates of them. As applications,we establish some generalizations and the equivalent forms of the Hilbert-type inequalitieswhose kernels are symmetric and homogeneous of1order. Also, the reverse forms andseveral particular results are considered. |
