On a Hilbert-type linear series operator and its applications |
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| Authors: | Jianjun Jin |
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| Institution: | a Department of Mathematics, Suzhou University, Suzhou, Jiangsu 215006, People's Republic of China
b Department of Mathematics, University of Texas-Pan American, Edinburg, TX 78539, USA |
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| Abstract: | 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. |
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| Keywords: | Hilbert-type series operator Hilbert-type inequalities Norm Weight coefficient Hö lder's inequality |
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