A note on Schrödinger operators with polynomial potentials

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Institute of Mathematics, Wrocław University, Plac Grunwaldzki 2/4 50-384 Wrocław, Poland

[D] J. Dziubański, A remark on a Marcinkiewicz-Hörmander multiplier theorem for some non-differential convolution operators, Colloq. Math. 58 (1989), 77-83.
[D1] J. Dziubański, Schwartz spaces associated with some non-differential convolution operators on homogeneous groups, ibid. 63 (1992), 153-161.
[DHJ] J. Dziubański, A. Hulanicki and J. Jenkins, A nilpotent Lie algebra and eigenvalue estimates, ibid. 68 (1995), 7-16.
[E] J. Epperson, Triebel-Lizorkin spaces for Hermite expansions, Studia Math. 114 (1995), 87-103.
[FeS] C. Fefferman and E. Stein, Some maximal inequalities, Amer. J. Math. 93 (1971), 107-115.
[FS] G. Folland and E. Stein, Hardy Spaces on Homogeneous Groups, Princeton Univ. Press, 1982.
[G] P. Głowacki, Stable semi-groups of measures as commutative approximate identities on non-graded homogeneous groups, Invent. Math. 83 (1986), 557-582.
[G1] P. Głowacki, The Rockland condition for nondifferential convolution operators II, Studia Math. 98 (1991), 99-114.
[He] W. Hebisch, On operators satisfying the Rockland condition, ibid. 131 (1998), 63-71.
[P] J. Peetre, On space of Triebel-Lizorkin type, Ark. Mat. 13 (1975), 123-130.
[Sh] Z. Shen, $L^{p}$ estimates for Schrödinger operators with certain potentials, Ann. Inst. Fourier (Grenoble) 45 (1995), 513-546.
[Z] J. Zhong, Harmonic analysis for some Schrödinger operators, Ph.D. thesis, Princeton Univ., 1993.