The weighted Hardy spaces associated to self-adjoint operators and their duality on product spaces

Suying Liu; Minghua Yang

Czechoslovak Mathematical Journal (2018)

  • Volume: 68, Issue: 2, page 415-431
  • ISSN: 0011-4642

Abstract

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Let L be a non-negative self-adjoint operator acting on L 2 ( ℝ n ) satisfying a pointwise Gaussian estimate for its heat kernel. Let w be an A r weight on ℝ n × ℝ n , 1 < r < ∞ . In this article we obtain a weighted atomic decomposition for the weighted Hardy space H L , w p ( ℝ n × ℝ n ) , 0 < p ≤ 1 associated to L . Based on the atomic decomposition, we show the dual relationship between H L , w 1 ( ℝ n × ℝ n ) and BMO L , w ( ℝ n × ℝ n ) .

How to cite

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Liu, Suying, and Yang, Minghua. "The weighted Hardy spaces associated to self-adjoint operators and their duality on product spaces." Czechoslovak Mathematical Journal 68.2 (2018): 415-431. <http://eudml.org/doc/294162>.

@article{Liu2018,
abstract = {Let $L$ be a non-negative self-adjoint operator acting on $L^2(\{\mathbb \{R\}\}^n)$ satisfying a pointwise Gaussian estimate for its heat kernel. Let $w$ be an $A_r$ weight on $\{\mathbb \{R\}\}^n\times \{\mathbb \{R\}\}^n$, $1<r<\infty $. In this article we obtain a weighted atomic decomposition for the weighted Hardy space $H^\{p\}_\{L,w\}(\{\mathbb \{R\}\}^n\times \{\mathbb \{R\}\}^n)$, $0<p\le 1$ associated to $L$. Based on the atomic decomposition, we show the dual relationship between $H^\{1\}_\{L,w\}(\{\mathbb \{R\}\}^n\times \{\mathbb \{R\}\}^n)$ and $\{\rm BMO\}_\{L,w\}(\{\mathbb \{R\}\}^n\times \{\mathbb \{R\}\}^n)$.},
author = {Liu, Suying, Yang, Minghua},
journal = {Czechoslovak Mathematical Journal},
keywords = {weighted Hardy space; operator; Gaussian estimate; duality; product space},
language = {eng},
number = {2},
pages = {415-431},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {The weighted Hardy spaces associated to self-adjoint operators and their duality on product spaces},
url = {http://eudml.org/doc/294162},
volume = {68},
year = {2018},
}

TY - JOUR
AU - Liu, Suying
AU - Yang, Minghua
TI - The weighted Hardy spaces associated to self-adjoint operators and their duality on product spaces
JO - Czechoslovak Mathematical Journal
PY - 2018
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 68
IS - 2
SP - 415
EP - 431
AB - Let $L$ be a non-negative self-adjoint operator acting on $L^2({\mathbb {R}}^n)$ satisfying a pointwise Gaussian estimate for its heat kernel. Let $w$ be an $A_r$ weight on ${\mathbb {R}}^n\times {\mathbb {R}}^n$, $1<r<\infty $. In this article we obtain a weighted atomic decomposition for the weighted Hardy space $H^{p}_{L,w}({\mathbb {R}}^n\times {\mathbb {R}}^n)$, $0<p\le 1$ associated to $L$. Based on the atomic decomposition, we show the dual relationship between $H^{1}_{L,w}({\mathbb {R}}^n\times {\mathbb {R}}^n)$ and ${\rm BMO}_{L,w}({\mathbb {R}}^n\times {\mathbb {R}}^n)$.
LA - eng
KW - weighted Hardy space; operator; Gaussian estimate; duality; product space
UR - http://eudml.org/doc/294162
ER -

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