scholarly journals Gaussian estimates with best constants for higher-order Schrödinger operators with Kato potentials

2016 ◽  
Vol 145 (1) ◽  
pp. 191-200
Author(s):  
G. Barbatis
Keyword(s):  
Schrödinger Operators ◽  
Higher Order ◽  
Best Constants ◽  
Schrodinger Operators ◽  
Gaussian Estimates

scholarly journals Long range scattering for higher order Schrödinger operators

2013 ◽  
Vol 254 (8) ◽  
pp. 3329-3351 ◽  
Author(s):  
Zhiwen Duan ◽  
Quan Zheng ◽  
Jing Feng
Keyword(s):  
Long Range ◽  
Schrödinger Operators ◽  
Higher Order ◽  
Schrodinger Operators

scholarly journals Sharp Gaussian Estimates for Heat Kernels of Schrödinger Operators

2019 ◽  
Vol 91 (1) ◽  
Author(s):  
Krzysztof Bogdan ◽  
Jacek Dziubański ◽  
Karol Szczypkowski
Keyword(s):  
Schrödinger Operators ◽  
Heat Kernels ◽  
Schrodinger Operators ◽  
Gaussian Estimates

scholarly journals Higher order eigenvalues for non-local Schrödinger operators

2018 ◽  
Vol 17 (1) ◽  
pp. 191-208 ◽  
Author(s):  
Niels Jacob ◽  
◽  
Feng-Yu Wang ◽  
◽  
Keyword(s):  
Schrödinger Operators ◽  
Higher Order ◽  
Schrodinger Operators ◽  
Non Local

scholarly journals Commutators of Higher Order Riesz Transform Associated with Schrödinger Operators

2013 ◽  
Vol 2013 ◽  
pp. 1-15 ◽  
Author(s):  
Yu Liu ◽  
Lijuan Wang ◽  
Jianfeng Dong
Keyword(s):  
Hardy Space ◽  
Schrödinger Operator ◽  
Schrödinger Operators ◽  
Riesz Transform ◽  
Higher Order ◽  
Schrodinger Operators ◽  
Schrodinger Operator ◽  
Reverse Hölder Class ◽  
Holder Class ◽  
Reverse Hölder

LetL=-Δ+Vbe a Schrödinger operator onℝn(n≥3), whereV≢0is a nonnegative potential belonging to certain reverse Hölder classBsfors≥n/2. In this paper, we prove the boundedness of commutatorsℛbHf=bℛHf-ℛH(bf)generated by the higher order Riesz transformℛH=∇2(-Δ+V)-1, whereb∈BMOθ(ρ), which is larger than the spaceBMO(ℝn). Moreover, we prove thatℛbHis bounded from the Hardy spaceHL1(ℝn)into weakLweak1(ℝn).

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