Multi-dimensional Fejér summability and local Hardy spaces
Volume 194 / 2009
Studia Mathematica 194 (2009), 181-195
MSC: Primary 42B08, 46E30; Secondary 42B30, 42A38.
DOI: 10.4064/sm194-2-5
Abstract
It is proved that the multi-dimensional maximal Fejér operator defined in a cone is bounded from the amalgam Hardy space $W(h_{p},\ell_\infty)$ to $W(L_{p},\ell_\infty)$. This implies the almost everywhere convergence of the Fejér means in a cone for all $f\in W(L_{1},\ell_\infty)$, which is larger than $L_1(\mathbb R^d)$.
