Some new Hardy-type inequalities on time scales

[摘要] In this paper, we will prove some new dynamic inequalities of Hardy-type on time scales. Some of the integral and difference inequalities that will be derived from our results in the continuous and discrete cases are original. The main results will be proved by using the dynamic Hölder inequality, integration by parts formula on time scales, and Keller’s chain rule on time scales. We will apply the main results to the continuous calculus, discrete calculus, and q-calculus as special cases.

[学科分类] 航空航天科学

[关键词] Hardy’s inequality;Dynamic inequality;Time scale