Weight characterizations for the discrete Hardy inequality with kernel

Abstract

A discrete Hardy-type inequality (For kernels of product type some scales of weight characterizations of the inequality are proved with the corresponding estimates of the best constant C. A sufficient condition for the inequality to hold in the general case is proved and this condition is necessary in special cases. Moreover, some corresponding results for the case when {a n } ∞ n=1 are replaced by the nonincreasing sequences {a * n } ∞ n=1 are proved and discussed in the light of some other recent results of this type.

An equivalence theorem for some integral conditions with general measures related to Hardy's inequality

“…This result is a generalization of a previous result of C.A. Okpoti, L.-E. Persson and A. Wedestig[9, Theorem 1]. At the endpoints of these scales we rediscover some previous results of G. Bennett[2].…”

“…, 5, and each s > 0.Remark 7.Another proof of Corollary 3 can be found in the Licentiate Thesis of C.A. Okpoti[7]. This result is a generalization of a previous result of C.A.…”

Applications of Taylor Series for Carleman's Inequality Through Hardy Inequality

“…In order to agree further with T. Carleman, other Mathematicians also proved the inequality (4) by different methods: Thus by differentiation and the variations of the Arithmetic (A n )-Geometric (G n ) mean inequality (i.e. G n ≤ A n ) methods (See [5], [6] [13], [14], [15] and the references therein).…”

Criteria of boundedness and compactness of a class of matrix operators

“…Lemma 2.2 can be proved in the same way as Lemma 2.1. For the proof of our main theorem we will need the following well-known result for the discrete weighted Hardy inequality (see [1,9]) and the criteria of precompactness of sets in l p (see [10, p. 32…”