Hardy type estimates for commutators of fractional integrals associated with Schrodinger operators
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Authors
Yinhong Xia
- School of Mathematics and Statistics, Huanghuai University, Zhumadian 463000, P. R. China.
Min Chen
- School of Mathematics and Statistics, Huanghuai University, Zhumadian 463000, P. R. China.
Abstract
We consider the Schrödinger operator \(L = -\Delta + V\) on \(\mathbb{R}^n\), where \(n \geq 3\) and the nonnegative potential \(V\) belongs to
reverse Hölder class \(RH_{q1}\) for some \(q_1 > n/2\) . Let \(I_\alpha\) be the fractional integral associated with \(L\), and let \(b\) belong to a new
Campanato space \(\Lambda_\beta^\theta(\rho)\). In this paper, we establish the boundedness of the commutators \([b, I_\alpha]\) from \(L^p(R^n)\) to \(L^q(R^n)\)
whenever \(1/q=1/p-(\alpha+\beta)/n, 1<p<n/(\alpha+\beta)\). When \(\frac{n}{n+\beta}<p\leq 1,1/q=1/p-(\alpha+\beta)/n\), we show that \([b, I_\alpha]\) is
bounded from \(H^p_
L(R^n)\) to \(L^q(R^n)\). Moreover, we also prove that \([b, I_\alpha]\) maps \(H_L^{\frac{n}{n+\beta}}(R^n)\) continuously into weak \(L^{\frac{n}{n-\alpha}}(R^n)\).
Share and Cite
ISRP Style
Yinhong Xia, Min Chen, Hardy type estimates for commutators of fractional integrals associated with Schrodinger operators, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 6, 3155--3167
AMA Style
Xia Yinhong, Chen Min, Hardy type estimates for commutators of fractional integrals associated with Schrodinger operators. J. Nonlinear Sci. Appl. (2017); 10(6):3155--3167
Chicago/Turabian Style
Xia, Yinhong, Chen, Min. "Hardy type estimates for commutators of fractional integrals associated with Schrodinger operators." Journal of Nonlinear Sciences and Applications, 10, no. 6 (2017): 3155--3167
Keywords
- Schrödinger operator
- commutator
- Campanato space
- fractional integral
- Hardy space.
MSC
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