From dyadic $Λ_α$ to $Λ_α$
In this paper we show how to compute the $Λ_α$ norm, $α\ge 0$, using the dyadic grid. This result is a consequence of the description of the Hardy spaces $H^p(R^N)$ in terms of dyadic and special atoms.
math.CA↗
arXiv subjects
Wael Abu-Shammala
Publications and source records attributed to Wael Abu-Shammala.
The Hardy-Lorentz Spaces $H^{p,q}(R^n)$
In this paper we consider the Hardy-Lorentz spaces $H^{p,q}(R^n)$, with $0<p\le 1$, $0<q\le \infty$. We discuss the atomic decomposition of the elements in these spaces, their interpolation properties, and the behavior of singular integrals and other operators acting on them.
math.CA↗
Characterizations of the Hardy Space $H^1$ and BMO
We describe the spaces $H^1(R)$ and BMO$(R)$ in terms of their closely related, simpler dyadic and two-sided counterparts. As a result of these characterizations we establish when a bounded linear operator defined on dyadic or two-sided $H^1(R)$ into a Banach space has a continuous extension to $H^1(R)$ and when a bounded linear operator that maps a Banach space into dyadic or two-sided BMO$(R)$ actually maps continuously into BMO$(R)$.
math.FA↗