A NEW MULTIPLE HILBERT-TYPE INTEGRAL INEQUALITY WITH A NON-HOMOGENEOUS FORM
ZENG ZHENG
Foshan University, Guangdong, 512005, P. R. China
XIE ZITIAN *
Department of Mathematics, Zhaoqing University, Zhaoqing, Guangdong, 526061, P. R. China
LIU XINGDONG
Department of Mathematics, Zhaoqing University, Zhaoqing, Guangdong, 526061, P. R. China
*Author to whom correspondence should be addressed.
Abstract
By applying methods of weight functions and techniques of real analysis. We prove a multidimensional Hilbert-type integral inequality with the best possible constant factor related to Ψ function, the multiple Hilbert-type integral inequality with a non-homogeneous form. As its applications, we consider the operator expressions and a some particular results to the non-homogeneous kernels and a homogeneous kernel of degree 0.
Keywords: Multiple Hilbert-type integral inequality, weight function, Holder's inequality, no-homogeneous form