Weighted weak type inequalities for modified Hardy operators and geometric means operators in dimensions one and greater

Optimal Hardy–littlewood Type Inequalities for Polynomials and Multilinear Operators

Abstract. In this paper we obtain quite general and definitive forms for Hardy–Littlewood type inequalities. Moreover, when restricted to the original particular cases, our approach provides much simpler and straightforward proofs and we are able to show that in most cases the exponents involved are optimal. The technique we used is a combination of probabilistic tools and of an interpolative a...

Weighted Composition Operators and Integral-Type Operators between Weighted Hardy Spaces on the Unit Ball

Compact Weighted Composition Operators and Multiplication Operators between Hardy Spaces

Weighted Weak Type Inequalities for the Hardy Operator When

The paper studies the weighted weak type inequalities for the Hardy operator as an operator from weighted L to weighted weak L in the case p = 1. It considers two different versions of the Hardy operator and characterizes their weighted weak type inequalities when p = 1. It proves that for the classical Hardy operator, the weak type inequality is generally weaker when q < p = 1. The best consta...

Hardy Type Inequalities Related to Degenerate Elliptic Differential Operators

We prove some Hardy type inequalities related to quasilinear second order degenerate elliptic differential operators Lpu := −∇ ∗ L(|∇Lu| ∇Lu). If φ is a positive weight such that −Lpφ ≥ 0, then the Hardy type inequality c ∫ Ω |u| φp |∇Lφ| p dξ ≤ ∫