Atomic decomposition of variable Hardy spaces via Littlewood-Paley-Stein theory (Q1697811)

In this paper, a new atomic decomposition for variable Hardy spaces \(H^{p(\cdot)}\), with \(0<p^{-}\leq p^+<\infty\), is established via the discrete Littlewood-Paley-Stein theory. This decomposition is applied to prove that every linear operator bounded on \(L^q\), \(1<q<\infty\), and \(H^{p(\cdot)}\), can be extended to a bounded operator from \(H^{p(\cdot)}\) to \(L^{p(\cdot)}\).