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A Hilbert-Type Inequality with Some Parameters and the Integral in Whole Plane
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Advances in Pure Mathematics·Volume 01 (2011)·Pages 84–89·Published 19 May 2011·DOI10.4236/apm.2011.13019
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Abstract
In this paper, by introducing some parameters and estimating the weight coefficient, we give a new Hilbert’s inequality with the integral in whole plane and with a non-homogeneous and the equivalent form is given as well. The best constant factor is calculated by the way of Complex Analysis.
KeywordsHilbert-Type Integral InequalityWeight FunctionHolder’s Inequality
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