On a Hilbert-Type Operator with a Class of Homogeneous Kernels

On a Hilbert-Type Operator with a Class of Homogeneous Kernels

Bicheng Yang Department of Mathematics, Guangdong Education Institute, Guangzhou, Guangdong 510303, China Correspondence should be addressed to Bicheng Yang, [email protected] Received 15 September 2008; Accepted 20 February 2009 Recommended by Patricia J. Y. Wong By using the way of weight coefficient and the theory of operators, we define a Hilbert-type operator with a class of homog...

On a Hardy-Hilbert-Type Inequality with a General Homogeneous Kernel

By the method of weight coefficients and techniques of real analysis, a Hardy-Hilbert-type inequality with a general homogeneous kernel and a best possible constant factor is given. The equivalent forms, the operator expressions with the norm, the reverses and some particular examples are also considered.

A class of Artinian local rings of homogeneous type

‎Let $I$ be an ideal in a regular local ring $(R,n)$‎, ‎we will find‎ ‎bounds on the first and the last Betti numbers of‎ ‎$(A,m)=(R/I,n/I)$‎. ‎if $A$ is an Artinian ring of the embedding‎ ‎codimension $h$‎, ‎$I$ has the initial degree $t$ and $mu(m^t)=1$‎, ‎we call $A$ a {it $t-$extended stretched local ring}‎. ‎This class of‎ ‎local rings is a natural generalization of the class of stretched ...

On a Hilbert-Type Operator with a Symmetric Homogeneous Kernel of −1-Order and Applications

on a hardy-hilbert-type inequality with a general homogeneous kernel

by the method of weight coefficients and techniques of real analysis, ahardy-hilbert-type inequality with a general homogeneous kernel and a bestpossible constant factor is given. the equivalent forms, the operatorexpressions with the norm, the reverses and some particular examples are alsoconsidered.