On dual spaces of anisotropic Hardy spaces

2012 ◽  
Vol 285 (17-18) ◽  
pp. 2078-2092 ◽  
Author(s):  
Shai Dekel ◽  
Tal Weissblat
Keyword(s):  
Hardy Spaces ◽  
Dual Spaces

scholarly journals Multiplication between Hardy spaces and their dual spaces

2019 ◽  
Vol 131 ◽  
pp. 130-170 ◽  
Author(s):  
Aline Bonami ◽  
Jun Cao ◽  
Luong Dang Ky ◽  
Liguang Liu ◽  
Dachun Yang ◽  
...  
Keyword(s):  
Hardy Spaces ◽  
Dual Spaces

scholarly journals Dual spaces of anisotropic mixed-norm Hardy spaces

2018 ◽  
Vol 147 (3) ◽  
pp. 1201-1215 ◽  
Author(s):  
Long Huang ◽  
Jun Liu ◽  
Dachun Yang ◽  
Wen Yuan
Keyword(s):  
Hardy Spaces ◽  
Mixed Norm ◽  
Dual Spaces

scholarly journals Dual Spaces of Multiparameter Local Hardy Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Wei Ding ◽  
Feng Yu
Keyword(s):  
Hardy Spaces ◽  
Duality Theory ◽  
Carleson Measure ◽  
Dual Spaces ◽  
Local Hardy Spaces ◽  
The Relationship

In this paper, we study the duality theory of the multiparameter local Hardy spaces h p ℝ n 1 × ℝ n 2 , and we prove that h p ℝ n 1 × ℝ n 2 ∗ = cm o p ℝ n 1 × ℝ n 2 , where cm o p ℝ n 1 × ℝ n 2 are defined by discrete Carleson measure. Moreover, we discuss the relationship among cm o p ℝ n 1 × ℝ n 2 , Li p p ℝ n 1 × ℝ n 2 , and rectangle cm o rect p ℝ n 1 × ℝ n 2 .

Weighted Carleson Measure Spaces Associated with Different Homogeneities

2014 ◽  
Vol 66 (6) ◽  
pp. 1382-1412 ◽  
Author(s):  
Xinfeng Wu
Keyword(s):  
Hardy Spaces ◽  
Carleson Measure ◽  
Forthcoming Paper ◽  
Weighted Hardy Spaces ◽  
Dual Spaces ◽  
Measure Spaces

AbstractIn this paper, we introduce weighted Carleson measure spaces associated with different homogeneities and prove that these spaces are the dual spaces of weighted Hardy spaces studied in a forthcoming paper. As an application, we establish the boundedness of composition of two Calderón–Zygmund operators with different homogeneities on the weighted Carleson measure spaces; this, in particular, provides the weighted endpoint estimates for the operators studied by Phong–Stein.

scholarly journals DUAL SPACES OF MULTI-PARAMETER MARTINGALE HARDY SPACES

2016 ◽  
Vol 67 (1) ◽  
pp. 137-145 ◽  
Author(s):  
Ferenc Weisz
Keyword(s):  
Hardy Spaces ◽  
Dual Spaces

Dual Spaces of Weighted Multi-Parameter Hardy Spaces Associated with the Zygmund Dilation

2012 ◽  
Vol 12 (3) ◽  
Author(s):  
Xiaolong Han ◽  
Guozhen Lu ◽  
Yayuan Xiao
Keyword(s):  
Hardy Spaces ◽  
Duality Theorem ◽  
Dual Spaces

AbstractIn this paper, we apply the discrete Littlewood-Paley-Stein analysis to prove the duality theorem of weighted multi-parameter Hardy spaces associated with Zygmund dilations, i.e., (HpZ (ω))∗ = CMO

scholarly journals Real-variable characterizations of Orlicz-slice Hardy spaces

2019 ◽  
Vol 17 (04) ◽  
pp. 597-664 ◽  
Author(s):  
Yangyang Zhang ◽  
Dachun Yang ◽  
Wen Yuan ◽  
Songbai Wang
Keyword(s):  
Hardy Spaces ◽  
Real Variable ◽  
Maximal Functions ◽  
Text Type ◽  
Dual Spaces ◽  
Hardy Type ◽  
Sublinear Operators ◽  
Special Cases ◽  
Type Spaces ◽  
Amalgam Spaces

In this paper, the authors first introduce a class of Orlicz-slice spaces which generalize the slice spaces recently studied by Auscher et al. Based on these Orlicz-slice spaces, the authors then introduce a new kind of Hardy-type spaces, the Orlicz-slice Hardy spaces, via the radial maximal functions. This new scale of Orlicz-slice Hardy spaces contains the variant of the Orlicz–Hardy space of Bonami and Feuto as well as the Hardy-amalgam space of de Paul Ablé and Feuto as special cases. Their characterizations via the atom, the molecule, various maximal functions, the Poisson integral and the Littlewood–Paley functions are also obtained. As an application of these characterizations, the authors establish their finite atomic characterizations, which further induce a description of their dual spaces and a criterion on the boundedness of sublinear operators from these Orlicz-slice Hardy spaces into a quasi-Banach space. Then, applying this criterion, the authors obtain the boundedness of [Formula: see text]-type Calderón–Zygmund operators on these Orlicz-slice Hardy spaces. All these results are new even for slice Hardy spaces and, moreover, for Hardy-amalgam spaces, the Littlewood–Paley function characterizations, the dual spaces and the boundedness of [Formula: see text]-type Calderón–Zygmund operators on these Hardy-type spaces are also new.

Sign in / Sign up

Export Citation Format

Share Document