Equivalent Conditions of a Hilbert-Type Multiple Integral Inequality Holding. (15th April 2020)

• Record Type: Journal Article
• Authors: Liao, Jianquan; Hong, Yong; Yang, Bicheng
• Other Names: Ólafsson Gestur Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2020(2020)
• Publication Date: 2020-04-15
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2020/3050952
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : Let ∑ i = 1 n 1 / p i = 1 p i > 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 + n K x 1, ⋯, x n ∏ i = 1 n f i x i d x 1 ⋯ d x n ≤ M ∏ i = 1 n f i p i, α i with homogeneous kernel K x 1, ⋯, x n of order λ is ∑ i = 1 n α i / p i = 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.