Intrinsic Square Function Characterizations of Hardy Spaces with Variable Exponents
By Ciqiang Zhuo, Dachun Yang, Yiyu Liang. Bulletin of the Malaysian Mathematical Sciences Society, 2014
88 citations recorded by the source corpus.
Let p(·):Rn→(0,∞)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p(\cdot ):\ \mathbb R^n\rightarrow (0,\infty )$$\end{document} be a measurable function satisfying some decay condition and some locally log-Hölder continuity. In this article, through first establishing characterizations of the variable exponent Hardy space Hp(·)(Rn)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H^{p(\cdot )}(\mathbb R^n)$$\end{document} in terms of the Littlewood–Paley g-function, the Lusin area function, and the gλ∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$g_\lambda ^*$$\end{document}-function, the authors then obtain its intrinsic square function characterizations including the intrinsic Littlewood–Paley g-function, the intrinsic Lusin area function, and the intrinsic gλ∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$g_\lambda ^*$$\end{document}-function. The p(·)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p(\cdot )$$\end{document}-Carleson measure characterization for the dual space of Hp(·)(Rn)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H^{p(\cdot )}(\mathbb R^n)$$\end{document}, the variable exponent Campanato space L1,p(·),s(Rn)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {L}_{1,p(\cdot ),s}(\mathbb R^n)$$\end{document}, in terms of the intrinsic function is also presented.
Subfields: Applied Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/3bea7eef1e4a9b0de5188bd23c728431bc9ebb31
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Citations in the corpus
- Variable Hardy–Lorentz spaces Hp(·),q(Rn) (2018, unknown): “[55] established the equivalent Mathematische Nachrichten.”
- Anisotropic Variable Hardy-Lorentz Spaces and Their Real Interpolation (2017, unknown): “g [23] with some weaker assumptions on p(·) than those used in [54], extended the theory of variable Lebesgue spaces via investigating the variable Hardy spaces on Rn. Later, Sawano [66], Zhuo et al. [85] and Yang et al. [81] further completed the theory of these variable Hardy spaces. For more deve”
- Characterizations of variable exponent Hardy spaces via Riesz transforms (2015, background): “[31] established their equivalent characterizations via intrinsic square functions, including the intrinsic Lusin area function, the intrinsic g-function and the intrinsic g∗ λ-function.”
- Variable weak Hardy spaces and their applications (2016, background): “[46] established equivalent characterizations of Hp(·)(Rn) via intrinsic square functions including the intrinsic Lusinarea function, the intrinsic Littlewood-Paley g-function or g∗ λ-function.”