Lusin Area Function and Molecular Characterizations of Musielak-Orlicz Hardy Spaces and Their Applications

By S. Hou, Dachun Yang, Sibei Yang. 2012

78 citations recorded by the source corpus.

Lusin Area Function and Molecular Characterizations of Musielak-Orlicz Hardy Spaces and Their ApplicationsLet $\varphi: \mathbb R^n\times [0,\infty)\to[0,\infty)$ be a growth function such that $\varphi(x,\cdot)$ is nondecreasing, $\varphi(x,0)=0$, $\varphi(x,t)>0$ when $t>0$, $\lim_{t\to\infty}\varphi(x,t)=\infty$, and $\varphi(\cdot,t)$ is a Muckenhoupt $A_\infty(\mathbb{R}^n)$ weight uniformly in $t$. In this paper, the authors establish the Lusin area function and the molecular characterizations of the Musielak-Orlicz Hardy space $H_\varphi(\mathbb{R}^n)$ introduced by Luong Dang Ky via the grand maximal function. As an application, the authors obtain the $\varphi$-Carleson measure characterization of the Musielak-Orlicz ${\mathop\mathrm{BMO}}$-type space $\mathop\mathrm{BMO}_{\varphi}(\mathbb{R}^n)$, which was proved to be the dual space of $H_\varphi(\mathbb{R}^n)$ by Luong Dang Ky.

Subfields: Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/9a7c84a4d2926b49a10fdd11ff93564c10de8990

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In Applied Mathematics

1. Dachun Yang
2. Yiyu Liang
3. Ciqiang Zhuo
4. Sibei Yang
5. Wen Yuan
6. Luong Dang Ky
7. The Anh Bui
8. Jizheng Huang

Citations in the corpus

• Musielak-Orlicz-Hardy Spaces Associated with Operators Satisfying Reinforced Off-Diagonal Estimates (2013, background): “Furthermore, several real-variable characterizations of the Hardy spaces of Musielak-Orlicz type were established in [42, 56].”
• Musielak–Orlicz–Hardy Spaces Associated with Operators and Their Applications (2012, methodology): “We remark that the method used to obtain the atomic characterization of the MusielakOrlicz-Hardy space Hφ,L(X ) in this paper is different from that in [86], but more close to the method in [54, 15, 57].”
• New real-variable characterizations of Musielak-Orlicz Hardy spaces (2012, methodology): “Furthermore, the Lusin area function and the molecular characterizations of Hφ(Rn) were obtained in [17].”
• Intrinsic Square Function Characterizations of Hardy Spaces with Variable Exponents (2014, methodology): “2), but tp(·) is not a uniformly Muckenhoupt weight, which was required in [23] (and hence [18, 26]).”
• Musielak-Orlicz Campanato Spaces and Applications (2013, methodology): “To obtain the φ-Carleson measure characterization of Lφ,1,s(R n), we need to recall the Musielak-Orlicz tent space introduced in [18].”
• New Hardy Spaces of Musielak–Orlicz Type and Boundedness of Sublinear Operators (2011, unknown): “Recently, new Hardy spaces of Musielak-Orlicz type have developed in many directions (see [11, 50, 53, 60, 61]), some their charcterizations and applications were also established and studied in [11, 53, 28, 40].”