A Maximal Function Characterization of H p on the Space of Homogeneous Type

1980 ◽  
Vol 262 (2) ◽  
pp. 579 ◽  
Author(s):  
Akihito Uchiyama
Keyword(s):  
Maximal Function ◽  
Space Of Homogeneous Type ◽  
Homogeneous Type ◽  
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 Some Function Spaces Relative to Morrey-Campanato Spaces on Metric Spaces

2005 ◽  
Vol 177 ◽  
pp. 1-29 ◽  
Author(s):  
Dachun Yang
Keyword(s):  
Sobolev Spaces ◽  
Maximal Function ◽  
Metric Spaces ◽  
Function Spaces ◽  
Sharp Maximal Function ◽  
Embedding Theorems ◽  
Homogeneous Type ◽  
Spaces Of Homogeneous Type ◽  
Lizorkin Space

In this paper, the author introduces the Morrey-Campanato spaces Lsp(X) and the spaces Cps(X) on spaces of homogeneous type including metric spaces and some fractals, and establishes some embedding theorems between these spaces under some restrictions and the Besov spaces and the Triebel-Lizorkin spaces. In particular, the author proves that Lsp(X) = Bs∞,∞(X) if 0 < s < ∞ and µ(X) < ∞. The author also introduces some new function spaces Asp(X) and Bsp(X) and proves that these new spaces when 0 < s < 1 and 1 < p < ∞ are just the Triebel-Lizorkin space Fsp,∞(X) if X is a metric space, and the spaces A1p(X) and B1p(X) when 1 < p < ∞ are just the Hajłasz-Sobolev spaces W1p(X). Finally, as an application, the author gives a new characterization of the Hajłasz-Sobolev spaces by making use of the sharp maximal function.

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 $p\in (0,1]$.

Sign in / Sign up

Export Citation Format

Share Document