On Hardy-type integral inequalities in the whole plane related to the extended Hurwitz-zeta function

[摘要] Using weight functions, we establish a few equivalent statements of two kinds of Hardy-type integral inequalities with nonhomogeneous kernel in the whole plane. The constant factors related to the extended Hurwitz-zeta function are proved to be the best possible. In the form of applications, we deduce some special cases involving homogeneous kernel. We additionally consider some particular inequalities and operator expressions.

[学科分类] 电力

[关键词] Hardy-type integral inequality;Weight function;Equivalent form;Operator;Hurwitz-zeta function