On a Hilbert-type linear series operator and its applications

This paper deals with a Hilbert-type linear series operator and its norm. Several generalizations of the Hilbert-type inequalities whose kernels are symmetric and homogeneous of the first order are presented. Included are applications of some new extended Hilbert-type inequalities with the best poss...

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Bibliographic Details
Published in:	Journal of mathematical analysis and applications Vol. 371; no. 2; pp. 691 - 704
Main Authors:	Jin, Jianjun, Debnath, Lokenath
Format:	Journal Article
Language:	English
Published:	Amsterdam Elsevier Inc 01-11-2010 Elsevier
Subjects:	Exact sciences and technology Hilbert-type inequalities Hilbert-type series operator Hölder's inequality Mathematical analysis Mathematics Norm Operator theory Sciences and techniques of general use Weight coefficient Hilbert-type series operator Norm Hilbert-type inequalities Weight coefficient Hölder's inequality Mathematical analysis Holder inequality Linear operator
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Summary:	This paper deals with a Hilbert-type linear series operator and its norm. Several generalizations of the Hilbert-type inequalities whose kernels are symmetric and homogeneous of the first order are presented. Included are applications of some new extended Hilbert-type inequalities with the best possible constant factors and the equivalent forms are established. Also, the reverse forms and some particular forms are obtained as special cases of the results of this paper.
ISSN:	0022-247X 1096-0813
DOI:	10.1016/j.jmaa.2010.06.002