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2 results

  • MATRIX-VARIATE GAUSS HYPERGEOMETRIC DISTRIBUTION

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  • ARJUN K. GUPTA, DAYA K. NAGAR
  • Journal:
    Journal of the Australian Mathematical Society / Volume 92 / Issue 3 / June 2012
    Published online by Cambridge University Press:
    04 March 2012, pp. 335-355
    Print publication:
    June 2012
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  • In this paper, we propose a matrix-variate generalization of the Gauss hypergeometric distribution and study several of its properties. We also derive probability density functions of the product of two independent random matrices when one of them is Gauss hypergeometric. These densities are expressed in terms of Appell’s first hypergeometric function F1 and Humbert’s confluent hypergeometric function Φ1of matrix arguments.

  • INEQUALITIES OF THE HILBERT TYPE IN $\mathbb{R}^{n}$ WITH NON-CONJUGATE EXPONENTS

  • Aleksandra Čižmešija, Ivan Perić, Predrag Vuković
  • Journal:
    Proceedings of the Edinburgh Mathematical Society / Volume 51 / Issue 1 / February 2008
    Published online by Cambridge University Press:
    04 February 2008, pp. 11-26
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  • In this paper we state and prove a new general Hilbert-type inequality in $\mathbb{R}^{n}$ with $k\geq2$ non-conjugate exponents. Using Selberg's integral formula, this result is then applied to obtain explicit upper bounds for the doubly weighted Hardy–Littlewood–Sobolev inequality and some further Hilbert-type inequalities for $k$ non-negative functions and non-conjugate exponents.