Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
|
   
Available in electronic format
Available in print format 		Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(e) ISSN 0002-9939(p)

     

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

Author(s): Kazuhiro Kurata; Seiichi Nishigaki; Satoko Sugano
Journal: Proc. Amer. Math. Soc. 128 (2000), 1125-1134.
MSC (1991): Primary 35B45, 42B20; Secondary 35J10
Posted: August 5, 1999
MathSciNet review: 1646196
Retrieve article in: PDF
This article is available free of charge

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 $W$.

References:

[Ad]
D. Adams, A note on Riesz potentials, Duke Math. J. 42(1975), 765-778.

[CF]
F.Chiarenza, M.Frasca, Morrey spaces and Hardy-Littlewood maximal function, Rend. Mat. 7(1987), 273-279. MR 90f:42017

[GR]
J. García-Cuerva, J. L. Rubio de Francia, Weighted Norm Inequalities and Related Topics, North-Holland, 1985.

[Gu]
D.Guibourg, Inégalitës maximales pour l'opérateur de Schrödinger, C.R. Acad.Sci.Paris, 316(1993), 249-252. MR 93k:35053

[He]
D.Henry, Geometric Theory of semilinear parabolic equations, Springer Lect. Note, No. 840, 1981. MR 83j:35084

[Ku]
S.T.Kuroda, Spectral Theory II(in Japanese), Iwanami-Shoten, 1979. MR 88a:35169

[KS]
K.Kurata, S.Sugano, A remark on estimates for uniformly elliptic operators on weighted $L^p$ spaces and Morrey spaces, preprint.

[Mi]
T. Mizuhara, Boundedness of some classical operators on generalized Morrey spaces, Harmonic Analysis (S.Igari, Ed.) ICM 90 Satellite Proceedings, Springer-Verlag, Tokyo(1991), 183-189. MR 95c:46039

[Na]
E. Nakai, Hardy-Littlewood maximal operator, singular integral operators and the Riesz potentials on generalized Morrey spaces, Math. Nachr. 166(1994), 95-103. MR 95k:42030

[Ok]
N. Okazawa, On the perturbation of linear operators in Banach and Hilbert spaces, J.Math.Soc.Japan, 34, 1982, 677-701. MR 84i:47021

[Ol]
P.A.Olsen, Fractional Integration, Morrey spaces and a Schrödinger equations, Comm. in P.D.E., 20(1995), 2005-2055. MR 97a:35042

[Sh1]
Z.Shen, $L^p$ estimates for Schrödinger operators with certain potentials, Ann. Inst. Fourier, Grenoble 45, 2(1995), 513-546. MR 96h:35037

[Sh2]
Z.Shen, Estimates in $L^p$ for Magnetic Schrödinger Operators, Indiana Univ. Math. J., 45(1996), 817-841. MR 97k:35043

[Ta]
M.Taylor, Microlocal Analysis on Morrey spaces, Preprint.

Similar Articles:

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 35B45, 42B20, 35J10

Retrieve articles in all Journals with MSC (1991): 35B45, 42B20, 35J10

Additional Information:

Kazuhiro Kurata
Affiliation: Department of Mathematics, Tokyo Metropolitan University, 1-1 Minami-Ohsawa, Hachioji-shi, Tokyo 192-0397, Japan
Email: kurata@comp.metro-u.ac.jp

Seiichi Nishigaki
Affiliation: Numazu College of Technology, 3600 Ooka Numazu 410-8501, Japan
Email: nishiga@la.numazu-ct.ac.jp

Satoko Sugano
Affiliation: Department of Mathematics, Gakushuin University, 1-5-1 Mejiro, toshima-ku, Tokyo 171, Japan
Email: 95243001@gakushuin.ac.jp

DOI: 10.1090/S0002-9939-99-05208-9
PII: S 0002-9939(99)05208-9
Received by editor(s): June 1, 1998
Posted: 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
Copyright of article: Copyright 2000, American Mathematical Society




AMS and Social Media LinkedIn Facebook Podcasts Twitter YouTube RSS Feeds Blogs Wikipedia