... norm of some Hilbert’sty pe linear operators.ThemainpurposeofthisarticleistostudythenormofaHilbert’stypelinearoperator with the kernel Amin{x, y}+ B max{x, y} andgivesomenewgeneralizationsofHilbert’sinequality. ... inequality, we obtain (2.6). For ε>0sufficiently small, set fε(x) = x(−1−ε)/2,forx ∈ [1,∞); fε(x) = 0, for x ∈ (0,1).Then gε(y) = y(−1−ε)/2,fory ∈ [1,∞); gε(y) = 0, for y ∈ (0,1). Assume ... Inequalities and ApplicationsVolume 2007, Article ID 82138, 10 pagesdoi:10.1155/2007/82138Research Article Hilbert’s Type Linear Operator and Some Extensions of Hilbert’s InequalityYongjin Li, Zhiping...