On maximal inequalities via comparison principle

Geometric inequalities via a general comparison principle for interacting gases

A Terminal Comparison Principle for Differential Inequalities

Maximal Inequalities for Associated Random Variables

In a celebrated work by Shao [13] several inequalities for negatively associated random variables were proved. In this paper we obtain some maximal inequalities for associated random variables. Also we establish a maximal inequality for demimartingales which generalizes and improves the result of Christofides [4].

A Liouville comparison principle for solutions of quasilinear differential inequalities

This work is devoted to the study of a Liouville comparison principle for entire weak solutions of quasilinear differential inequalities of the form A(u) + |u|q−1u ≤ A(v) + |v|q−1v on Rn, where n ≥ 1, q > 0, and the operator A(w) belongs to a class of the so-called α-monotone operators. Typical examples of such operators are the p-Laplacian and its well-known modifications for 1 < p ≤ 2. The re...

On Maximal Inequalities Arising in Best Approximation

Let f be a function in an Orlicz space L and μ(f,L) be the set of all the best Φ-approximants to f, given a σ−lattice L. Weak type inequalities are proved for the maximal operator f∗ = supn |fn|, where fn is any selection of functions in μ(f,Ln), and Ln is an increasing sequence of σ-lattices. Strong inequalities are proved in an abstract set up which can be used for an operator as f∗.