Some (<em>p, q</em>)-Hardy type inequalities for (<em>p, q</em>)-integrable functions

Abstract

In this paper, we study some $(p,q)$-Hardy type inequalities for $(p,q)$-integrable functions. Moreover, we also study $(p,q)$-Hölder integral inequality and $(p,q)$-Minkowski integral inequality for two variables. By taking $p=1$ and $q\to 1$, our results reduce to classical results on Hardy type inequalities, Hölder integral inequality and Minkowski integral inequality for two variables.

Keywords

• hardy type inequalities
• minkowski integral inequality
• (<i>p
• q</i>)-calculus
• q</i>)-integrable function