Weighted Weak Type Inequalities for the Hardy Operator When
نویسندگان
چکیده
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 constant in the inequality is also estimated.
منابع مشابه
Some functional inequalities in variable exponent spaces with a more generalization of uniform continuity condition
Some functional inequalities in variable exponent Lebesgue spaces are presented. The bi-weighted modular inequality with variable exponent $p(.)$ for the Hardy operator restricted to non- increasing function which is$$int_0^infty (frac{1}{x}int_0^x f(t)dt)^{p(x)}v(x)dxleqCint_0^infty f(x)^{p(x)}u(x)dx,$$ is studied. We show that the exponent $p(.)$ for which these modular ine...
متن کاملBilateral composition operators on vector-valued Hardy spaces
Let $T$ be a bounded operator on the Banach space $X$ and $ph$ be an analytic self-map of the unit disk $Bbb{D}$. We investigate some operator theoretic properties of bilateral composition operator $C_{ph, T}: f ri T circ f circ ph$ on the vector-valued Hardy space $H^p(X)$ for $1 leq p leq +infty$. Compactness and weak compactness of $C_{ph, T}$ on $H^p(X)$ are characterized an...
متن کاملWeighted iteratedHardy-type inequalities
In this paper a reduction and equivalence theorems for the boundedness of the composition of a quasilinear operator T with the Hardy and Copson operators in weighted Lebesgue spaces are proved. New equivalence theorems are obtained for the operator T to be bounded in weighted Lebesgue spaces restricted to the cones of monotone functions, which allow to change the cone of non-decreasing function...
متن کاملThe Weighted Space Odyssey
The common topic of this thesis is boundedness of integral and supremal operators between function spaces with weights. The results of this work have the form of characterizations of validity of weighted operator inequalities for appropriate cones of functions. The outcome can be divided into three categories according to the particular type of studied operators and function spaces. The first p...
متن کاملSharp estimates for the p-adic Hardy type operators on higher-dimensional product spaces
In this paper, we introduce the p-adic Hardy type operator and obtain its sharp bound on the p-adic Lebesgue product spaces. Meanwhile, an analogous result is computed for the p-adic Lebesgue product spaces with power weights. In addition, we characterize a sufficient and necessary condition which ensures that the weighted p-adic Hardy type operator is bounded on the p-adic Lebesgue product spa...
متن کامل