Discrete Hardy Inequality Research Articles

DISCRETE HARDY-TYPE INEQUALITY WITH KERNEL

Necessary and sufficient conditions are given for the validity of discrete Hardy's inequality for the sum of two discrete Hardy-type operators with not necessary non-negative coefficients.

APPLICATIONS OF TAYLOR SERIES FOR CARLEMAN'S INEQUALITY THROUGH HARDY INEQUALITY

In this paper, we prove the discrete Hardy inequality through the continuous case for decreasing functions using elementary properties of calculus. Also, we prove the Carleman's inequality through limiting the discrete Hardy inequality with applications of Taylor series.

The [formula omitted]-adic weighted Hardy–Cesàro operator and an application to discrete Hardy inequalities

This paper aims to investigate the boundedness of the p-adic analog of the weighted Hardy–Cesàro operator Uψ,s:f→∫Zp⋆f(s(t)⋅)ψ(t)dt on weighted Lebesgue spaces and weighted BMO spaces. In each case, we obtain the corresponding operator norms |Uψ,s|. In particular, these results have a surprising relevance to discrete Hardy inequalities on the real field. We prove a reverse BMO–Hardy inequality and give a necessary condition on ψ so that the commutator of Uψ,s is bounded on Lωr(Qpn) with symbols in BMOω(Qpn).

Two-sided Hardy-type inequalities for monotone functions

We consider Hardy-type operators on the cones of monotone functions with general positive σ-finite Borel measure. Some two-sided Hardy-type inequalities are proved for the parameter −∞ < p < ∞. It is pointed out that such equivalences, in particular, imply a new characterization of the discrete Hardy inequality for the (most difficult) case 0 < q < p ≤ 1.

Weight characterizations for the discrete Hardy inequality with kernel

A discrete Hardy-type inequality is considered for a positive kernel , , and . For kernels of product type some scales of weight characterizations of the inequality are proved with the corresponding estimates of the best constant . 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 are replaced by the nonincreasing sequences are proved and discussed in the light of some other recent results of this type.

On weighted discrete Hardy's inequality for negative power numbers

In this paper we consider the weighted discrete Hardy’s inequality for different real power numbers 0 = r < 1 and obtain some new refinements of its finite sections. For r < −1 our results improve those previously given by Nguyen et al. in [19, 20]. Moreover, we prove that the constant factors involved in the right-hand sides of the obtained inequalities are the best possible, that is, they cannot be replaced with any smaller constant. Mathematics subject classification (2000): 26D15.

Two-Dimensional Discrete Hardy Inequalities

A sufficient condition on nonnegative double-sequences $$\nu = \left( {\nu \left( {n_1 ,n_2 } \right)} \right)_{n_1 ,n_2 } \quad {\text{and}}\quad U = \left( {U\left( {n_1 ,n_2 } \right)} \right)_{n_1 ,n_2 }$$ is derived in order that the two-dimensional discrete Hardy operator His bounded from \(\ell ^p \left( \nu \right)\) into \(\ell ^q \left( U \right)\) whenever 1 < p ≦ q < ∞.

A MANY VARIABLE GENERALIZATION OF THE DISCRETE HARDY'S INEQUALITY

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On the Discrete Hardy Inequality

On the Discrete Hardy Inequality