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2 results

  • A Hilbert inequality and an Euler-Maclaurin summation formula

  • Mario Krnić, Josip Pečarić
  • Journal:
    The ANZIAM Journal / Volume 48 / Issue 3 / January 2007
    Published online by Cambridge University Press:
    17 February 2009, pp. 419-431
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  • We obtain a generalized discrete Hilbert and Hardy-Hilbert inequality with non-conjugate parameters by means of an Euler-Maclaurin summation formula. We derive some general results for homogeneous functions and compare our findings with existing results. We improve some earlier results and apply the results to some special homogeneous functions.

  • 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.