The Hardy-Littlewood-PSlya （HLP） inequality [1] states that if a ∈ lp, b ∈ 1q and In this article, we prove the HLP inequality in the case where A = 1,p = q = 2 with a logarithm correction, as conjectured by Ding ...The Hardy-Littlewood-PSlya （HLP） inequality [1] states that if a ∈ lp, b ∈ 1q and In this article, we prove the HLP inequality in the case where A = 1,p = q = 2 with a logarithm correction, as conjectured by Ding [2]：In addition, we derive an accurate estimate for the best constant for this inequality.展开更多
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, Polya, D＇Apuzzo, Sbordone and Popoli...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, Polya, D＇Apuzzo, Sbordone and Popoli. We also apply these inequalities to prove a higher integrability theorem for decreasing functions on time scales.展开更多
基金supported by the NSF grants DMS-0908097 and EAR-0934647
文摘The Hardy-Littlewood-PSlya （HLP） inequality [1] states that if a ∈ lp, b ∈ 1q and In this article, we prove the HLP inequality in the case where A = 1,p = q = 2 with a logarithm correction, as conjectured by Ding [2]：In addition, we derive an accurate estimate for the best constant for this inequality.
文摘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, Polya, D＇Apuzzo, Sbordone and Popoli. We also apply these inequalities to prove a higher integrability theorem for decreasing functions on time scales.
