Lp ESTIMATES FOR SCHR¨ODINGER TYPE OPERATORS ON THE HEISENBERG GROUP
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We investigate the Schr¨odinger type operator [수식] on the Heisenberg group [수식]is the sublaplacian and the nonnegative potential V belongs to the reverse H¨older class Bq for [수식] where Q is the homogeneous dimension of Hn. We shall establish the estimates of the fundamental solution for the operator H2 and obtain the Lp estimates for the operator [수식], where rHn is the gradient operator on Hn.
Abstract
We investigate the Schr¨odinger type operator [수식] on the Heisenberg group [수식]is the sublaplacian and the nonnegative potential V belongs to the reverse H¨older class Bq for [수식] where Q is the homogeneous dimension of Hn. We shall establish the estimates of the fundamental solution for the operator H2 and obtain the Lp estimates for the operator [수식], where rHn is the gradient operator on Hn.
참고문헌 (14)
- C. Benson, "Fundamental solutions for powers of the Heisenberg sub-Laplacian", Illinois J. Math., 37(3), pp.455~476 (1993)
- C. Berenstein, "Laguerre Calculus And its Applications on The Heisenberg Group" (2001), American Mathematical Society, International press
- T. Coulhon, "About Riesz transforms on the Heisenberg groups", Math. Ann., 305(2), pp.369~379 (1996)
- C. Fefferman, "The uncertainty principle", Bull. Amer. Math. Soc. (N.S.), 9(2), pp.129~206 (1983)
- G. B. Folland, "Hardy Spaces on Homogeneous Groups, Mathematical Notes, 28" (1982), Princeton University Press, University of Tokyo Press
- F. Gehring, "The Lp-integrability of the partial derivatives of a quasiconformal mapping", Acta Math., 130, pp.265~277 (1973)
- D. Jerison, "Estimates for the heat kernel for a sum of squares of vector fields", Indiana Univ. Math. J., 35(4), pp.835~854 (1986)
- H. Q. Li, "Estimations Lp des op´erateurs de Schr¨odinger sur les groupes nilpotents", J. Funct. Anal., 161(1), pp.152~218 (1999)
- N. Lohou´e, "Estim´ees de type Hardy-Sobolev sur certaines vari´et´es riemanniennes et les groupes de Lie", J. Funct. Anal., 112(1), pp.121~158 (1993)
- G. Z. Lu, "A Fefferman-Phong type inequality for degenerate vector fields and applications", Panamer. Math. J., 6(4), pp.37~57 (1996)
- Z. W. Shen, "Lp estimates for Schrodinger operators with certain potentials", Ann. Inst. Fourier (Grenoble), 45(2), pp.513~546 (1995)
- Z. W. Shen, "On the Neumann problem for Schrodinger operators in Lipschitz domains", Indiana Univ. Math. J., 43(1), pp.143~176 (1994)
- S. Sugano, "Lp estimates for some Schr¨odinger operators and a Calder´on-Zygmund operator of Schr¨odinger type", Tokyo J. Math., 30(1), pp.179~197 (2007)
- J. P. Zhong, "Harmonic analysis for some Schr¨odinger type operators", 박사, pp.1993