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Boundedness of integral operators
on generalized Morrey spaces
and its application to Schrödinger operators

Authors: Kazuhiro Kurata, Seiichi Nishigaki and Satoko Sugano
Journal: Proc. Amer. Math. Soc. 128 (2000), 1125-1134
MSC (1991): Primary 35B45, 42B20; Secondary 35J10
Published electronically: August 5, 1999
MathSciNet review: 1646196
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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper, we study boundedness of integral operators on generalized Morrey spaces and its application to estimates in Morrey spaces for the Schrödinger operator $L_2=-\Delta +V(x)+W(x)$ with nonnegative $V\in (RH)_{\infty}$ (reverse Hölder class) and small perturbed potentials $W$.

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Additional Information

Kazuhiro Kurata
Affiliation: Department of Mathematics, Tokyo Metropolitan University, 1-1 Minami-Ohsawa, Hachioji-shi, Tokyo 192-0397, Japan

Seiichi Nishigaki
Affiliation: Numazu College of Technology, 3600 Ooka Numazu 410-8501, Japan

Satoko Sugano
Affiliation: Department of Mathematics, Gakushuin University, 1-5-1 Mejiro, toshima-ku, Tokyo 171, Japan

Received by editor(s): June 1, 1998
Published electronically: August 5, 1999
Additional Notes: The first author was partially supported by Grant-in Aid for Scientific Research (C)(No. 09640208), the Ministry of Education, Science, Sports and Culture.
Communicated by: Christopher D. Sogge
Article copyright: © Copyright 2000 American Mathematical Society