Bull. Korean Math. Soc. 2024; 61(2): 489-509
Online first article March 18, 2024 Printed March 31, 2024
https://doi.org/10.4134/BKMS.b230191
Copyright © The Korean Mathematical Society.
Yao He
Central South University
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
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