scholarly journals Boundedness of classical Calderón-Zygmund convolution operators on product Hardy space

2013 ◽  
Vol 20 (3) ◽  
pp. 591-599 ◽  
Author(s):  
Chaoqiang Tan
Keyword(s):  
Hardy Space ◽  
Convolution Operators ◽  
Product Hardy Space

Weighted product Hardy space associated with operators

2020 ◽  
Vol 15 (4) ◽  
pp. 649-683
Author(s):  
Qingquan Deng ◽  
Djalal Eddine Guedjiba
Keyword(s):  
Hardy Space ◽  
Product Hardy Space

scholarly journals Various characterizations of product Hardy space

2011 ◽  
Vol 139 (12) ◽  
pp. 4385-4400 ◽  
Author(s):  
Ji Li ◽  
Liang Song ◽  
Chaoqiang Tan
Keyword(s):  
Hardy Space ◽  
Product Hardy Space

Duality theory of weighted Hardy spaces with arbitrary number of parameters

2014 ◽  
Vol 26 (5) ◽  
Author(s):  
Guozhen Lu ◽  
Zhuoping Ruan
Keyword(s):  
Hardy Space ◽  
Hardy Spaces ◽  
Arbitrary Number ◽  
Duality Theory ◽  
Weak Condition ◽  
Weighted Hardy Spaces ◽  
Duality Result ◽  
Product Hardy Space ◽  
Product Weight

AbstractIn this paper, we use the discrete Littlewood–Paley–Stein analysis to get the duality result of the weighted product Hardy space for arbitrary number of parameters under a rather weak condition on the product weight

Marstrand's Approximate Independence of Sets and Strong Differentiation of the Integral

2016 ◽  
Vol 119 (1) ◽  
pp. 92
Author(s):  
Raquel Cabral
Keyword(s):  
Hardy Space ◽  
Euclidean Space ◽  
Positive Measure ◽  
Low Complexity ◽  
Constructive Proof ◽  
Cantelli Lemma ◽  
Negative Function ◽  
Almost Everywhere ◽  
Product Hardy Space ◽  
L Log L

A constructive proof is given for the existence of a function belonging to the product Hardy space $H^1(\mathsf{R} \times \mathsf{R})$ and the Orlicz space $L(\log L)^{\epsilon}(\mathsf{R}^{2})$ for all $0<\epsilon <1$, for all whose integral is not strongly differentiable almost everywhere on a set of positive measure. It consists of a modification of a non-negative function created by J. M. Marstrand. In addition, we generalize the claim concerning "approximately independent sets" that appears in his work in relation to hyperbolic-crosses. Our generalization, which holds for any sets with boundary of sufficiently low complexity in any Euclidean space, has a version of the second Borel-Cantelli Lemma as a corollary.

The maximal operator of the Marcinkiewicz-Fejér means of the 2-dimensional Vilenkin-Fourier series

2008 ◽  
Vol 45 (3) ◽  
pp. 321-331
Author(s):  
István Blahota ◽  
Ushangi Goginava
Keyword(s):  
Fourier Series ◽  
Hardy Space ◽  
Maximal Operator ◽  
Fejér Means

In this paper we prove that the maximal operator of the Marcinkiewicz-Fejér means of the 2-dimensional Vilenkin-Fourier series is not bounded from the Hardy space H2/3 ( G2 ) to the space L2/3 ( G2 ).

Sign in / Sign up

Export Citation Format

Share Document