Maximal function characterization of Hp for the bidisc

1980 ◽  
pp. 51-58 ◽  
Author(s):  
R. F. Gundy
Keyword(s):  
Maximal Function ◽  
Function Characterization

Non-tangential Maximal Function Characterizations of Hardy Spaces Associated with Degenerate Elliptic Operators

2015 ◽  
Vol 67 (5) ◽  
pp. 1161-1200 ◽  
Author(s):  
Junqiang Zhang ◽  
Jun Cao ◽  
Renjin Jiang ◽  
Dachun Yang
Keyword(s):  
Hardy Space ◽  
Maximal Function ◽  
Hardy Spaces ◽  
Riesz Transform ◽  
Degenerate Elliptic Operators ◽  
Degenerate Elliptic Operator ◽  
Muckenhoupt Class ◽  
Degenerate Elliptic ◽  
Function Characterization

AbstractLet w be either in the Muckenhoupt class of A2(ℝn) weights or in the class of QC(ℝn) weights, and let be the degenerate elliptic operator on the Euclidean space ℝn, n ≥ 2. In this article, the authors establish the non-tangential maximal function characterization of the Hardy space associated with , and when with , the authors prove that the associated Riesz transform is bounded from to the weighted classical Hardy space .

scholarly journals A maximal function characterization of the class $H\sp{p}$

1971 ◽  
Vol 157 ◽  
pp. 137-137
Author(s):  
D. L. Burkholder ◽  
R. F. Gundy ◽  
M. L. Silverstein
Keyword(s):  
Maximal Function ◽  
Function Characterization

scholarly journals A maximal function characterization of the Hardy space for the Gauss measure

2012 ◽  
Vol 141 (5) ◽  
pp. 1679-1692 ◽  
Author(s):  
Giancarlo Mauceri ◽  
Stefano Meda ◽  
Peter Sjögren
Keyword(s):  
Hardy Space ◽  
Maximal Function ◽  
Gauss Measure ◽  
Function Characterization

A Maximal Function Characterization of the Class H p

1971 ◽  
Vol 157 ◽  
pp. 137 ◽  
Author(s):  
D. L. Burkholder ◽  
R. F. Gundy ◽  
M. L. Silverstein
Keyword(s):  
Maximal Function ◽  
Function Characterization

LITTLEWOOD–PALEY CHARACTERIZATIONS OF ANISOTROPIC WEAK MUSIELAK–ORLICZ HARDY SPACES

2018 ◽  
Vol 237 ◽  
pp. 39-78
Author(s):  
BO LI ◽  
RUIRUI SUN ◽  
MINFENG LIAO ◽  
BAODE LI
Keyword(s):  
Hardy Space ◽  
Maximal Function ◽  
Hardy Spaces ◽  
Growth Function ◽  
Anisotropic Growth ◽  
Area Function ◽  
Function Characterization ◽  
Lusin Area Function ◽  
Classical Hardy Space

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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