Abstract:
Using the weight function methods, the equivalent parameter conditions for the validity of Hilbert-type integral inequalities with non-homogeneous kernel
K(
x,
y)=
φλ(
xλ1yλ2)
φ′(
xλ1yλ2) and the best constant factor are discussed. The necessary and sufficient conditions for constructing such Hilbert-type inequalities and the formula for expressing the best constant factor are obtained. Many new Hilbert-type integral inequalities with some specific non-homogeneous kernels and the best constant factors are also obtained. Finally, the norm and boundedness of corresponding singular integral operators are discussed.