Anisotropic weak Hardy spaces of Musielak-Orlicz type and their applications

Zhang, Hui; Qi, Chunyan; Li, Baode

doi:10.1007/s11464-016-0546-7

Cited by 7 publications

(16 citation statements)

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“…[41] and the anisotropic weak Musielak–Orlicz Hardy space of Zhang et al. [55] and Qi et al. [47], we introduce the anisotropic weak Musielak–Orlicz Hardy space which includes all of the above mentioned weak spaces (see Remark 2.8 below for more details).…”

Section: Introductionmentioning

confidence: 99%

“…Zhang et al. [55, Theorem 1] obtained the atomic characterization of with respect to a particular anisotropic growth function , that is, the anisotropic -growth function of uniformly lower type and of uniformly upper type , where . In this article, motivated by Liang et al.…”

Section: Introductionmentioning

confidence: 99%

“…[41, Theorem 3.5], we obtain the atomic characterization of with respect to a general anisotropic growth function of uniformly lower type and of uniformly upper type 1. Hence, we cannot directly use the method with respect to the uniformly upper property of in [55, Theorem 1]. We overcome this difficulty via using a more general superposition principle of weak type estimates (see Lemma 3.2 below) and establishing a more subtle estimate of Schwartz function on weighted anisotropic Campanato space (see Lemma 3.5 below).…”

Section: Introductionmentioning

confidence: 99%

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Littlewood–paley Characterizations of Anisotropic Weak Musielak–orlicz Hardy Spaces

Li¹,

Sun²,

Liao³

et al. 2018

Nagoya Math. J.

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Let $A$ be an expansive dilation on $\mathbb{R}^{n}$ and $\unicode[STIX]{x1D711}:\mathbb{R}^{n}\times [0,\infty )\rightarrow [0,\infty )$ an anisotropic growth function. In this article, the authors introduce the anisotropic weak Musielak–Orlicz Hardy space $\mathit{WH}_{A}^{\unicode[STIX]{x1D711}}(\mathbb{R}^{n})$ via the nontangential grand maximal function and then obtain its Littlewood–Paley characterizations in terms of the anisotropic Lusin-area function, $g$-function or $g_{\unicode[STIX]{x1D706}}^{\ast }$-function, respectively. All these characterizations for anisotropic weak Hardy spaces $\mathit{WH}_{A}^{p}(\mathbb{R}^{n})$ (namely, $\unicode[STIX]{x1D711}(x,t):=t^{p}$ for all $t\in [0,\infty )$ and $x\in \mathbb{R}^{n}$ with $p\in (0,1]$) are new. Moreover, the range of $\unicode[STIX]{x1D706}$ in the anisotropic $g_{\unicode[STIX]{x1D706}}^{\ast }$-function characterization of $\mathit{WH}_{A}^{\unicode[STIX]{x1D711}}(\mathbb{R}^{n})$ coincides with the best known range of the $g_{\unicode[STIX]{x1D706}}^{\ast }$-function characterization of classical Hardy space $H^{p}(\mathbb{R}^{n})$ or its weighted variants, where $p\in (0,1]$.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Littlewood–paley Characterizations of Anisotropic Weak Musielak–orlicz Hardy Spaces

Li¹,

Sun²,

Liao³

et al. 2018

Nagoya Math. J.

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“…Very recently, Liang et al [34] introduced weak Musielak-Orlicz Hardy spaces via the vertical maximal function and established its atomic characterizations. Zhang et al [49] introduced the anisotropic weak Musielak-Orlicz Hardy space W H ϕ A (R n ) via the grand maximal function and obtained its atomic characterizations, where ϕ is a particular class of anisotropic growth function (see [49, p. 6] for more details). Liu et al [38,36] introduced the anisotropic variable Hardy-Lorentz space H…”

mentioning

confidence: 99%

“…and W H ϕ A, m is just weak Musielak-Orlicz Hardy space of Liang et al [34]. (iv) When ϕ is an anisotropic growth function with i(ϕ) = I(ϕ) = p, where p ∈ (0, 1], W H ϕ A, m is reduced to the anisotropic weak Musielak-Orlicz Hardy space of Zhang et al [49].…”

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confidence: 99%

Molecular characterization of anisotropic weak Musielak-Orlicz Hardy spaces and their applications

Sun¹,

Li²,

Li³

2019

Communications on Pure &Amp; Applied Analysis

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Let A be a real n × n matrix with all its eigenvalues λ satisfy |λ| > 1. Let ϕ : R n × [0, ∞) → [0, ∞) be an anisotropic Musielak-Orlicz function, i.e., ϕ(x, •) is an Orlicz function uniformly in x ∈ R n and ϕ(•, t) is an anisotropic Muckenhoupt A∞(R n) weight uniformly in t ∈ (0, ∞). In this article, the authors introduce the anisotropic weak Musielak-Orlicz Hardy space W H ϕ A (R n) via the grand maximal function and establish its molecular characterization which are anisotropic extensions of Liang, Yang and Jiang (Math. Nachr. 289: 634-677, 2016). As an application, the boundedness of anisotropic Calderón-Zygmund operators from H ϕ A (R n) to W H ϕ A (R n) in the critical case is presented.

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Weighted variable anisotropic Hardy spaces

2024

Anal.Math.Phys.

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Anisotropic weak Hardy spaces of Musielak-Orlicz type and their applications

Cited by 7 publications

References 20 publications

Littlewood–paley Characterizations of Anisotropic Weak Musielak–orlicz Hardy Spaces

Littlewood–paley Characterizations of Anisotropic Weak Musielak–orlicz Hardy Spaces

Molecular characterization of anisotropic weak Musielak-Orlicz Hardy spaces and their applications

Weighted variable anisotropic Hardy spaces

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