scholarly journals Weighted Weak Local Hardy Spaces Associated with Schrödinger Operators

2015 ◽  
Vol 2015 ◽  
pp. 1-9
Author(s):  
Hua Zhu
Keyword(s):  
Hardy Spaces ◽  
Atomic Decomposition ◽  
Critical Radius ◽  
Schrödinger Operators ◽  
Riesz Transforms ◽  
Schrodinger Operators ◽  
Local Hardy Spaces ◽  
Radius Function

We characterize the weighted weak local Hardy spacesWhρp(ω)related to the critical radius functionρand weightsω∈A∞ρ,∞(Rn)which locally behave as Muckenhoupt’s weights and actually include them, by the atomic decomposition. As an application, we show that localized Riesz transforms are bounded on the weighted weak local Hardy spaces.

scholarly journals Hardy Spaces Associated to Schrödinger Operators on Product Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Liang Song ◽  
Chaoqiang Tan
Keyword(s):  
Hardy Spaces ◽  
Atomic Decomposition ◽  
Schrödinger Operators ◽  
Nonnegative Function ◽  
Maximal Functions ◽  
Schrodinger Operators ◽  
Schrodinger Operator ◽  
Product Spaces ◽  
Area Integral ◽  
Lusin Area Integral

LetL=−Δ+Vbe a Schrödinger operator onℝn, whereV∈Lloc1(ℝn)is a nonnegative function onℝn. In this article, we show that the Hardy spacesLon product spaces can be characterized in terms of the Lusin area integral, atomic decomposition, and maximal functions.

scholarly journals AN ATOMIC DECOMPOSITION FOR HARDY SPACES ASSOCIATED TO SCHRÖDINGER OPERATORS

2011 ◽  
Vol 91 (1) ◽  
pp. 125-144 ◽  
Author(s):  
LIANG SONG ◽  
CHAOQIANG TAN ◽  
LIXIN YAN
Keyword(s):  
Hardy Space ◽  
Maximal Function ◽  
Hardy Spaces ◽  
Atomic Decomposition ◽  
Schrödinger Operators ◽  
Nonnegative Function ◽  
Schrodinger Operators ◽  
Integrable Functions ◽  
Function Characterization ◽  
Product Domains

AbstractLetL=−Δ+Vbe a Schrödinger operator on ℝnwhereVis a nonnegative function in the spaceL1loc(ℝn) of locally integrable functions on ℝn. In this paper we provide an atomic decomposition for the Hardy spaceH1L(ℝn) associated toLin terms of the maximal function characterization. We then adapt our argument to give an atomic decomposition for the Hardy spaceH1L(ℝn×ℝn) on product domains.

scholarly journals Endpoint estimates for Riesz transforms of magnetic Schrödinger operators

2006 ◽  
Vol 44 (2) ◽  
pp. 261-275 ◽  
Author(s):  
Xuan Thinh Duong ◽  
El Maati Ouhabaz ◽  
Lixin Yan
Keyword(s):  
Schrödinger Operators ◽  
Riesz Transforms ◽  
Schrodinger Operators
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