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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.
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참고문헌 (14)
참고문헌 신청
C. Benson / 1993 / Fundamental solutions for powers of the Heisenberg sub-Laplacian / Illinois J. Math. 37 (3) : 455 ~ 476
C. Berenstein / 2001 / Laguerre Calculus And its Applications on The Heisenberg Group / American Mathematical Society, International press
C. Fefferman / 1983 / The uncertainty principle / Bull. Amer. Math. Soc. (N.S.) 9 (2) : 129 ~ 206
D. Jerison / 1986 / Estimates for the heat kernel for a sum of squares of vector fields / Indiana Univ. Math. J. 35 (4) : 835 ~ 854
F. Gehring / 1973 / The Lp-integrability of the partial derivatives of a quasiconformal mapping / Acta Math. 130 : 265 ~ 277
C. Berenstein / 2001 / Laguerre Calculus And its Applications on The Heisenberg Group / American Mathematical Society, International press
C. Fefferman / 1983 / The uncertainty principle / Bull. Amer. Math. Soc. (N.S.) 9 (2) : 129 ~ 206
D. Jerison / 1986 / Estimates for the heat kernel for a sum of squares of vector fields / Indiana Univ. Math. J. 35 (4) : 835 ~ 854
F. Gehring / 1973 / The Lp-integrability of the partial derivatives of a quasiconformal mapping / Acta Math. 130 : 265 ~ 277
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