|
| NEW DYNAMIC INEQUALITIES FOR DECREASING FUNCTIONS AND THEOREMS OF HIGHER INTEGRABILITY |
| S.H. Saker,D. O'Regan,M.M. Osman,R.P. Agarwal |
| (Dept. of Math., Faculty of Science, Mansoura University, Mansoura-Egypt;School of Math., Statistics and Applied Math., National University of Ireland, Galway, Ireland;Dept. of Math., Texas A $\&$ M University- Kingsvilie, Texas, 78363, USA) |
| DOI： |
| Abstract: |
| In this paper we establish some new dynamic inequalities on time scales which contain in particular generalizations of integral and discrete inequalities due to
Hardy, Littlewood, P\'{o}lya, D'Apuzzo, Sbordone and Popoli. We also apply these inequalities to prove a higher integrability theorem for decreasing functions on time scales. |
| Key words: reverse H\"{o}lder's inequality; Gehring class; higher integrability; Hardy-Littlewood-P\'{o}lya inequality; time scales |