DISCRETE POINCARE-TYPE INEQUALITIES

Poincare Inequalities

Poincare inequalities are a simple way to obtain lower bounds on the distortion of mappings X into Y. These are shown below to be sharp when we consider the Lp spaces. A Poincare inequality is one of the following type: suppose Ψ : [0, ∞) → [0, ∞) is a nondecreasing function and that au,v, bu,v are finite arrays of real numbers (for u, v ∈ X, and not all of the numbers 0). We say that functions...

Bilinear Sobolev-Poincare inequalities and Leibniz-type rules

The dual purpose of this article is to establish bilinear Poincaré-type estimates associated to an approximation of the identity and to explore the connections between bilinear pseudo-differential operators and bilinear potential-type operators. The common underlying theme in both topics is their applications to Leibniz-type rules in Sobolev and Campanato-Morrey spaces under Sobolev scaling.

Some Discrete Poincaré-type Inequalities

Some discrete analogue of Poincaré-type integral inequalities involving many functions of many independent variables are established. These in turn can serve as generators of further interesting discrete inequalities. 2000 Mathematics Subject Classification. Primary 39A10, 39A12, 39B72.

New discrete Halanay-type inequalities and applications

In this paper, we introduce some new discrete type Halanay inequalities which extend the existing results. On the basis of these inequalities, we discuss the global stability of discrete neural networks with time-varying delays. © 2012 Elsevier Ltd. All rights reserved.

Volterra Discrete Inequalities of Bernoulli Type