Equivalent Conditions of a Hilbert-Type Multiple Integral Inequality Holding

摘要

Let ∑i=1n1/pi=1 pi1, 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.