publication . Preprint . 2004

Convex Hypersurfaces and $L^p$ Estimates for Schr\"odinger Equations

Zheng, Quan; Yao, Xiaohua; Fan, Da;
Open Access English
  • Published: 19 Mar 2004
Comment: 18 pages
free text keywords: Mathematics - Analysis of PDEs, Mathematics - Classical Analysis and ODEs, 35J10, 42B10
Download from

[4] M. Balabane and H. A. Emami-Rad, Lp estimates for Schr¨odinger evolution equations, Trans. Amer. Math. Soc. 292 (1985) 357-373.

[5] J. Bruna, A. Nagel, and S. Wainger, Convex hypersurfaces and Fourier transforms, Ann. Math. 127 (1988), 333-365.

[6] M. Cowling, S. Disney, G. Maucceri, and D. Mu¨ller, Damping oscillatory integrals, Invent. Math. 101 (1990) 237-260.

[7] G. Da Prato, Semigruppi regolarizzabili, Ricerche Mat. 15 (1966) 223-248.

[8] E. B. Davies and M. M. H. Pang, The Cauchy problem and a generalization of the Hille-Yosida theorem, Proc. London Math. Soc. 55 (1987) 181-208.

[9] M. Hieber, Integrated semigroups and differential operators on Lp, Dissertation, Tu¨bingen, 1989. [OpenAIRE]

[10] L. H¨ormander, Estimates for translation invariant operators in Lp spaces, Acta Math. 104 (1960) 93-140.

[11] A. Miyachi, On some estimates for the wave equation in Lp and Hp, J. Fac. Sci. Univ. Tokyo 27 (1980) 331-354. [OpenAIRE]

[12] A. Miyachi, On some singular Fourier multipliers, J. Fac. Sci. Univ. Tokyo 28 (1981) 267-315. [OpenAIRE]

[13] J. van Neerven and B. Straub, On the existence and growth of mild solutions of the abstract Cauchy problem for operators with polynomially bounded resolvent, Houston J. Math. 24 (1998) 137-171.

[14] M. Schechter, Operator Methods in Quantum Mechanics, Elsevier North Holland, New York, 1981.

[15] M. Schechter, Spectra of Partial Differential Operators, 2nd ed., Elsevier Science Publishers B.V., Amsterdam, 1986.

[16] E. M. Stein, Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals, Princeton Univ. Press, New Jersey, 1993.

[17] Q. Zheng, Abstract differential operators and Cauchy problems, Tu¨binger Berichte zur Funktionalanalysis 4 (1995) 273-280.

[18] Q. Zheng and Y. Li, Abstract parabolic systems and regularized semigroups, Pacific J. Math. 182 (1998) 183-199.

Powered by OpenAIRE Open Research Graph
Any information missing or wrong?Report an Issue