Document Type : Research Paper

Authors

1 Faculty of Material Sciences, University of Tiaret and Laboratory of Informatics and Mathematics, University of Tiaret-Algeria.

2 Department of Mathematics, University of Tiaret and Laboratory of Informatics and Mathematics, University of Tiaret-Algeria.

Abstract

Weighted integral inequalities for general integral operators on monotone positive functions with parameters $p$ and $q$ are established in [4]. The aim of this work is to extend the results to different cases of these parameters, in particular for negative $p$ and $q$. We give some new lemmas which will be frequently used in the proofs of the main theorems.

Keywords

[1] M. Arino and B. Muckenhoupt,  Maximal function on classical Lorenz spaces and Hardy's inequality with weights for non-increasing functions, Trans. Amer. Math. Soc., 320 (1990), pp. 727-735.
[2] B. Benaissa,  On the Reverse Minkowski's Integral Inequality, Kragujevac. J. Math., 46(3) (2022), pp. 407-416.
[3] C. Bennett and R. Sharpley,  Interpolation of operators. Math. 129, Academic Press, 1988.
[4]  Shanzhong. Lai,  Weighted norm inequalities for general operators on monotone functions, Amer. Math. Soc., 340(2) (1993), pp. 811-836.
[5] Bicheng. Yang,  On a new Hardy- type integral inequality, Int. Math. Forum., 2(67) (2007), pp. 3317-3322.