The weighted weak local Hardy spaces

Weak Hardy Spaces

We provide a careful treatment of the weak Hardy spaces Hp,∞(Rn) for all indices 0 < p < ∞. The study of these spaces presents differences from the study of the Hardy-Lorentz spaces H(R) for q <∞, due to the lack of a good dense subspace of them. We obtain several properties of weak Hardy spaces and we discuss a new square function characterization for them, obtained by He [16].

Extension of Hardy Inequality on Weighted Sequence Spaces

Let and be a sequence with non-negative entries. If , denote by the infimum of those satisfying the following inequality: whenever . The purpose of this paper is to give an upper bound for the norm of operator T on weighted sequence spaces d(w,p) and lp(w) and also e(w,?). We considered this problem for certain matrix operators such as Norlund, Weighted mean, Ceasaro and Copson ma...

Weak-star Convergence in Multiparameter Hardy Spaces

We prove a multiparameter version of a classical theorem of Jones and Journé on weak-star convergence in the Hardy space H.

Generalized composition operators on weighted 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...