The purpose of this paper is to give a new atomic decomposition for variable Hardy spaces via the discrete Littlewood–Paley–Stein theory. As an application of this decomposition, we assume that is a linear operator bounded on and , and we thus obtain that can be extended to a bounded operator from to .
"Atomic decomposition of variable Hardy spaces via Littlewood–Paley–Stein theory." Ann. Funct. Anal. 9 (1) 87 - 100, February 2018. https://doi.org/10.1215/20088752-2017-0026