Equivalent Conditions of a Hilbert-Type Multiple Integral Inequality Holding
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Let ∑i=1n1/pi=1pi>1, in this paper, by using the method of weight functions and technique of real analysis; it is proved that the equivalent parameter condition for the validity of multiple integral Hilbert-type inequality ∫R+nKx1,⋯,xn∏i=1nfixi dx1⋯dxn≤M∏i=1nfipi,αi with homogeneous kernel Kx1,⋯,xn of order λ is ∑i=1nαi/pi=λ+n−1, and the calculation formula of its optimal constant factor is obtained. The basic theory and method of constructing a Hilbert-type multiple integral inequality with the homogeneous kernel and optimal constant factor are solved.
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2012 ◽
Vol 4
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pp. 41-46
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2014 ◽
Vol 7
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pp. 9-17
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2017 ◽
Vol 2017
(1)
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