EQUIVALENT PROPERTIES OF A HILBERT-TYPE INTEGRAL INEQUALITY WITH THE BEST CONSTANT FACTOR RELATED TO THE HURWITZ ZETA FUNCTION

作者：Rassias, Michael^*; Yang, Bicheng

来源：Annals of Functional Analysis, 2018, 9(2): 282-295.

DOI：10.1215/20088752-2017-0031

• Hilbert-type integral inequality
• weight function
• Hurwitz zeta function
• equivalent form
• operator

By the use of methods of real analysis and weight functions, we study the equivalent properties of a Hilbert-type integral inequality with the nonhomogeneous kernel. The constant factor related to the Hurwitz zeta function is proved to be the best possible. As a corollary, a few equivalent conditions of a Hilbert-type integral inequality with the homogeneous kernel are deduced. We also consider their operator expressions.

• 出版日期2018-5
• 单位广东第二师范学院