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.

Weighted boundedness for Toeplitz type operator associated to general integral operators

2014 ◽  
Vol 07 (02) ◽  
pp. 1450026
Author(s):  
Lanzhe Liu
Keyword(s):  
Maximal Function ◽  
Integral Operators ◽  
Morrey Spaces ◽  
Type Operator ◽  
Sharp Maximal Function ◽  
Riesz Operator ◽  
Marcinkiewicz Operator ◽  
Bmo Functions ◽  
General Integral ◽  
Toeplitz Type Operator

In this paper, we establish the weighted sharp maximal function estimates for the Toeplitz type operators associated to some integral operators and the weighted Lipschitz and BMO functions. As an application, we obtain the boundedness of the Toeplitz type operators on weighted Lebesgue and Morrey spaces. The operator includes Littlewood–Paley operator, Marcinkiewicz operator and Bochner–Riesz operator.

On inclusion relation between weak Morrey spaces and Morrey spaces

2018 ◽  
Vol 168 ◽  
pp. 27-31
Author(s):  
Hendra Gunawan ◽  
Denny Ivanal Hakim ◽  
Eiichi Nakai ◽  
Yoshihiro Sawano
Keyword(s):  
Morrey Spaces ◽  
Inclusion Relation ◽  
Weak Morrey Spaces

scholarly journals Schrödinger type operators on local generalized Morrey spaces related to certain nonnegative potentials

2020 ◽  
Vol 25 (2) ◽  
pp. 671-690 ◽  
Author(s):  
Vagif S. Guliyev ◽  
◽  
Ramin V. Guliyev ◽  
Mehriban N. Omarova ◽  
Maria Alessandra Ragusa ◽  
...  
Keyword(s):  
Morrey Spaces ◽  
Generalized Morrey Spaces ◽  
Schrödinger Type Operators

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).

Sign in / Sign up

Export Citation Format

Share Document