no. 12
A Hardy type estimate with exponential weights
[Sur une estimation du type de Hardy avec des poids exponentiels]
Mǎntoiu, Marius1 ; Purice, Radu1
1 Institute of Mathematics “Simion Stoilow” of the Romanian Academy, PO Box 1-764, 70700 Bucharest, Romania
Comptes Rendus. Mathématique, Tome 335 (2002) no. 12, pp. 1023-1027.

Pour des opérateurs de la forme H=λ(−i∇)+V avec λ une fonction analytique dans une bande et à croissance polynomielle à l'infini, nous démontrons une estimation du type de Hardy dans L 2 (ℝ n ), avec des poids exponentiels. En effet nous étendons nos résultats précedents [5] du cas des fonctions λ analytiques bornées au cas à croissance polynomielle.

In this paper we consider operators of the form H=λ(−i∇)+V with λ analytic in a strip having some specific growth conditions at infinity and prove Hardy type estimates in L 2 (ℝ n ) with exponential weights. In fact we extend our previous results [5] from bounded analytic functions on a strip to analytic functions with polynomial growth in that strip.

Reçu le :
Publié le :
DOI : 10.1016/S1631-073X(02)02604-3
Mǎntoiu, Marius 1 ; Purice, Radu 1

1 Institute of Mathematics “Simion Stoilow” of the Romanian Academy, PO Box 1-764, 70700 Bucharest, Romania 
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Mǎntoiu, Marius; Purice, Radu. A Hardy type estimate with exponential weights. Comptes Rendus. Mathématique, Tome 335 (2002) no. 12, pp. 1023-1027. doi : 10.1016/S1631-073X(02)02604-3. http://www.numdam.org/articles/10.1016/S1631-073X(02)02604-3/

[1] Amrein, W.O.; Boutet de Monvel, A.; Georgescu, V. Hardy type inequalities for abstract differential operators, Mem. Amer. Math. Soc., Volume 70 (1987) no. 375, pp. 1-119

[2] Amrein, W.O.; Boutet de Monvel, A.; Georgescu, V. C0-Groups, Commutator Methods and Spectral Theory of N-Body Hamiltonians, Birkhäuser, 1996

[3] Hörmander, L. The Analysis of Linear Partial Differential Operators II, Springer-Verlag, 1983

[4] Hörmander, L. The Analysis of Linear Partial Differential Operators IV, Springer-Verlag, 1985

[5] Mǎntoiu, M.; Purice, R. Weighted estimations from a conjugate operator, Lett. Math. Phys., Volume 51 (2000), pp. 17-35

[6] Mǎntoiu, M.; Purice, R. A priori decay for eigenfunctions of perturbed periodic Schrödinger operators, Ann. H. Poincaré, Volume 2 (2001), pp. 525-551

[7] Mǎntoiu, M.; Purice, R. Hardy Type Inequalities, Mourre Estimate and A-Priori Decay for Eigenfunctions, Oper. Theory Adv. Appl., 126, Birkhäuser, 2001

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