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J. Korean Math. Soc. 2010; 47(3): 537-546

Printed May 1, 2010

https://doi.org/10.4134/JKMS.2010.47.3.537

Copyright © The Korean Mathematical Society.

Discrete multiple Hilbert type inequality with non-homogeneous kernel

Biserka Dra\v s\v ci\'c Ban, Josip Pe\v cari\'c, Ivan Peri\'c, and Tibor Pog\'any

University of Rijeka, University of Zagreb, University of Zagreb, and University of Rijeka

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Multiple discrete Hilbert type inequalities are established in the case of non-homogeneous kernel function by means of Laplace integral representation of associated Dirichlet series. Using newly derived integral expressions for the Mordell-Tornheim Zeta function a set of subsequent special cases, interesting by themselves, are obtained as corollaries of the main inequality.

Keywords: discrete Hilbert type inequality, discrete multiple Hilbert type inequality, Dirichlet-series, non-homogeneous kernel, homogeneous kernel, multiple H\"older inequality, Tornheim's double sum, Witten Zeta function, Mordell-Tornheim Zeta function

MSC numbers: Primary 26D15; Secondary 40B05, 40G99

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