L p estimates for Riesz transform and their commutators associated with Schrödinger type operator

2016 ◽  
Vol 31 (1) ◽  
pp. 112-126
Author(s):  
Xiao-li Chen ◽  
Jie-cheng Chen
Keyword(s):  
Riesz Transform ◽  
Type Operator ◽  
Schrödinger Type Operator

Riesz transform related to a Schrödinger type operator on the Heisenberg group

2015 ◽  
Vol 22 (3) ◽  
Author(s):  
Yu Liu ◽  
Wenjiang Xie
Keyword(s):  
Heisenberg Group ◽  
Riesz Transform ◽  
Type Operator ◽  
Schrödinger Type Operator

AbstractIn this paper, we consider the Schrödinger type operator

On the Completeness of the System of Normalized Eigenfunctions of a Nonlinear Schrödinger-Type Operator on a Segment

1997 ◽  
Vol 12 (01) ◽  
pp. 295-298 ◽  
Author(s):  
P. E. Zhidkov
Keyword(s):  
Type Operator ◽  
Nonlinear Schrödinger ◽  
Schrödinger Type Operator

In this note, a recent rigorous author's result on the completeness in the space L2 of the system of eigenfunctions of a nonlinear Schrödinger-type operator is established (without proof).

scholarly journals Fourth-order Schrödinger type operator with singular potentials

2016 ◽  
Vol 107 (3) ◽  
pp. 285-294 ◽  
Author(s):  
Federica Gregorio ◽  
Sebastian Mildner
Keyword(s):  
Fourth Order ◽  
Type Operator ◽  
Singular Potentials ◽  
Schrödinger Type Operator

scholarly journals Generic Simplicity of a Schrödinger-type Operator on the Torus

2017 ◽  
Vol 2 (1) ◽  
pp. 1-19
Author(s):  
Louis Omenyi ◽  
Emmanuel Nwaeze ◽  
McSylvester Omaba
Keyword(s):  
Type Operator ◽  
Schrödinger Type Operator

scholarly journals Wavelets, Sobolev Multipliers, and Application to Schrödinger Type Operators with Nonsmooth Potentials

2013 ◽  
Vol 2013 ◽  
pp. 1-22
Author(s):  
Pengtao Li ◽  
Qixiang Yang ◽  
Yueping Zhu
Keyword(s):  
Morrey Spaces ◽  
Type Operator ◽  
Inclusion Relation ◽  
Multiplier Space ◽  
Schrödinger Type Operator ◽  
Meyer Wavelets ◽  
Schrödinger Type Operators

We employ Meyer wavelets to characterize multiplier spaceXr,pt(ℝn)without using capacity. Further, we introduce logarithmic Morrey spacesMr,pt,τ(ℝn)to establish the inclusion relation between Morrey spaces and multiplier spaces. By fractal skills, we construct a counterexample to show that the scope of the indexτofMr,pt,τ(ℝn)is sharp. As an application, we consider a Schrödinger type operator with potentials inMr,pt,τ(ℝn).

scholarly journals Some Estimates of Schrödinger-Type Operators with Certain Nonnegative Potentials

2008 ◽  
Vol 2008 ◽  
pp. 1-8 ◽  
Author(s):  
Yu Liu ◽  
Youzheng Ding
Keyword(s):  
Weak Type ◽  
Type Operator ◽  
Reverse Hölder Class ◽  
Hölder Class ◽  
Weak Type Estimates ◽  
Holder Class ◽  
Schrödinger Type Operator ◽  
Schrödinger Type Operators ◽  
Reverse Hölder

We consider the Schrödinger-type operatorH=(−Δ)2+V2, where the nonnegative potentialVbelongs to the reverse Hölder classBq1forq1≥n/2,  n≥5. TheLpestimates of the operator∇4H−1related toHare obtained whenV∈Bq1and1<p≤q1/2. We also obtain the weak-type estimates of the operator∇4H−1under the same condition ofV.

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