Bulletin of the
Korean Mathematical Society BKMS

In this paper, let $q\in(0,1]$. We establish the boundedness of intrinsic $g$-functions from the Hardy-Lorentz spaces with variable exponent ${H}^{p(\cdot),q}(\mathbb R^{n})$ into Lorentz spaces with variable exponent ${L}^{p(\cdot),q}(\mathbb R^{n})$. Then, for any $q\in(0,1]$, via some estimates on a discrete Littlewood-Paley $g$-function and a Peetre-type maximal function, we obtain several equivalent characterizations of ${H}^{p(\cdot),q}(\mathbb R^{n})$ in terms of wavelets.

Keywords: Variable Hardy-Lorentz space, Peetre-type maximal function, Littlewood-Paley $g$-function, wavelet, atom

MSC numbers: Primary 42C40, 42B30; Secondary 42B25, 46E30