scholarly journals Maximal inequalities and Riesz transform estimates on L^p spaces for Schrödinger operators with nonnegative potentials

2007 ◽  
Vol 57 (6) ◽  
pp. 1975-2013 ◽  
Author(s):  
Pascal Auscher ◽  
Besma Ben Ali
Keyword(s):  
Schrödinger Operators ◽  
Riesz Transform ◽  
Schrodinger Operators ◽  
Maximal Inequalities

THE ESTIMATES OF RIESZ TRANSFORMS ASSOCIATED TO SCHRÖDINGER OPERATORS

2016 ◽  
Vol 101 (3) ◽  
pp. 290-309 ◽  
Author(s):  
QINGQUAN DENG ◽  
YONG DING ◽  
XIAOHUA YAO
Keyword(s):  
Schrödinger Operator ◽  
Schrödinger Operators ◽  
Riesz Transform ◽  
Riesz Transforms ◽  
Schrodinger Operators ◽  
Schrodinger Operator ◽  
Reverse Hölder Class ◽  
Holder Class ◽  
Small Norm ◽  
Reverse Hölder

Let$H=-\unicode[STIX]{x1D6E5}+V$be a Schrödinger operator with some general signed potential$V$. This paper is mainly devoted to establishing the$L^{q}$-boundedness of the Riesz transform$\unicode[STIX]{x1D6FB}H^{-1/2}$for$q>2$. We mainly prove that under certain conditions on$V$, the Riesz transform$\unicode[STIX]{x1D6FB}H^{-1/2}$is bounded on$L^{q}$for all$q\in [2,p_{0})$with a given$2<p_{0}<n$. As an application, the main result can be applied to the operator$H=-\unicode[STIX]{x1D6E5}+V_{+}-V_{-}$, where$V_{+}$belongs to the reverse Hölder class$B_{\unicode[STIX]{x1D703}}$and$V_{-}\in L^{n/2,\infty }$with a small norm. In particular, if$V_{-}=-\unicode[STIX]{x1D6FE}|x|^{-2}$for some positive number$\unicode[STIX]{x1D6FE}$,$\unicode[STIX]{x1D6FB}H^{-1/2}$is bounded on$L^{q}$for all$q\in [2,n/2)$and$n>4$.

Endpoint Estimates of Riesz Transforms Associated with Generalized Schrödinger Operators

2018 ◽  
Vol 61 (4) ◽  
pp. 787-801 ◽  
Author(s):  
Yu Liu ◽  
Shuai Qi
Keyword(s):  
Schrödinger Operator ◽  
Schrödinger Operators ◽  
Riesz Transform ◽  
Riesz Transforms ◽  
Schrodinger Operators ◽  
Schrodinger Operator ◽  
Hardy Type ◽  
Generalized Schrödinger Operator

AbstractIn this paper we establish the endpoint estimates and Hardy type estimates for the Riesz transform associated with the generalized Schrödinger operator.

scholarly journals The boundedness of commutator of Riesz transform associated with Schrödinger operators on a Hardy space

2009 ◽  
Vol 7 (3) ◽  
pp. 241-250
Author(s):  
Canqin Tang ◽  
Chuanmei Bi
Keyword(s):  
Hardy Space ◽  
Schrödinger Operator ◽  
Schrödinger Operators ◽  
Riesz Transform ◽  
Schrodinger Operators ◽  
Schrodinger Operator ◽  
Type Function

In this paper, we study the boundedness of commutator[b,T]of Riesz transform associated with Schrödinger operator andbisBMOtype function, note that the kernel ofThas no smoothness, and the boundedness fromHb1(Rn)→L1(Rn)is obtained.

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