Equivalent Parameter Conditions for the Validity of Half-Discrete Hilbert-Type Multiple Integral Inequality with Generalized Homogeneous Kernel. (11th August 2020) - Chen, Qiang; He, Bing; Hong, Yong; Li, Zhen
Abstract : Let G u, v be a homogeneous nonnegative function of order λ, K n, x m, ρ = G n λ 1, x m, ρ λ 2 . By using the weight coefficient method, the equivalent parameter conditions and best constant factors for the validity of the following half-discrete Hilbert-type multiple integral inequality ∫ ℝ + m   ∑ n = 1 ∞   K n, x m, ρ a n f x d x ≤ M a ~ p, α f q, β are discussed. Finally, its applications in operator theory are discussed.