Boundedness of higher order Riesz transforms associated with Schrödinger type operator on generalized Morrey spaces

Volume 10, Issue 5, pp 2757--2766 http://dx.doi.org/10.22436/jnsa.010.05.42

Publication Date: May 25, 2017 Submission Date: April 07, 2017

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Authors

Bijun Ren - Department of Information Engineering, Henan Institute of Finance and Banking, Zhengzhou, 451464, P. R. China. Hui Wang - Teachers College, Nanyang Institute of Technology, Nanyang, 473000, P. R. China.

Abstract

Let \(L_2 = (-\Delta)^2 + V^2\) be a Schrödinger type operator, where \(V \neq 0\) is a non-negative potential and belongs to the reverse Hölder class \(RH_q\) for \(q \geq n/2, n\geq 5\). The higher Riesz transform associated with \(L_2\) is denoted by \(R = \nabla^2L_2^{\frac{-1}{2}}\) and its dual is denoted by \(R^* =L_2^{\frac{-1}{2}} \nabla^2\). In this paper, we investigate the boundedness of higher Riesz transforms and their commutators on the generalized Morrey spaces related to some non-negative potential.

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ISRP Style

Bijun Ren, Hui Wang, Boundedness of higher order Riesz transforms associated with Schrödinger type operator on generalized Morrey spaces, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 5, 2757--2766

AMA Style

Ren Bijun, Wang Hui, Boundedness of higher order Riesz transforms associated with Schrödinger type operator on generalized Morrey spaces. J. Nonlinear Sci. Appl. (2017); 10(5):2757--2766

Chicago/Turabian Style

Ren, Bijun, Wang, Hui. "Boundedness of higher order Riesz transforms associated with Schrödinger type operator on generalized Morrey spaces." Journal of Nonlinear Sciences and Applications, 10, no. 5 (2017): 2757--2766

Keywords

Schrödinger operator
Riesz transform
commutator
BMO
generalized Morrey space.

MSC

42B35
35J10

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