scholarly journals Boundedness of second order Riesz transforms associated to Schrödinger operators on Musielak-Orlicz-Hardy spaces

2014 ◽  
Vol 13 (4) ◽  
pp. 1435-1463 ◽  
Author(s):  
Jun Cao ◽  
Der-Chen Chang ◽  
Dachun Yang ◽  
Sibei Yang
Keyword(s):  
Hardy Spaces ◽  
Schrödinger Operators ◽  
Second Order ◽  
Riesz Transforms ◽  
Schrodinger Operators

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 Regularity for the second order Riesz transforms associated with Schrödinger operators on weighted BMO type spaces

2018 ◽  
Vol 20 ◽  
pp. 02005
Author(s):  
Trong Nguyen Ngoc ◽  
Dao Nguyen Anh ◽  
L. X. Truong
Keyword(s):  
Schrödinger Operator ◽  
Schrödinger Operators ◽  
Hölder’S Inequality ◽  
Second Order ◽  
Riesz Transforms ◽  
Schrodinger Operators ◽  
Schrodinger Operator ◽  
Weighted Bmo ◽  
Type Spaces ◽  
Weighted Case

Let L = −Δ + V be a Schrödinger operator on ℝn, where V is a nonnegative potential satisfying the suitable reverse Hölder’s inequality. In this paper, we study the boundedness of the second order Riesz transforms such as L−1∇2 on the spaces of BMO type for weighted case. We generalized the known results to the weighted case.

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