Glasnik Matematicki, Vol. 47, No. 2 (2012), 373-379.

GLOBAL SPACE-TIME L^p-ESTIMATES FOR THE AIRY OPERATOR ON L²(R²) AND SOME APPLICATIONS

Aicha Chaban and Mohammed Hichem Mortad

Département de Mathématiques, Université d'Oran (Es-senia), B.P. 1524, El Menouar, Oran 31000, Algeria
e-mail: mhmortad@gmail.com, mortad@univ-oran.dz

Abstract.   Let L be the Airy operator. The aim of this paper is to prove some a priori estimates for L defined as an unbounded operator on L²(R²). Some applications and counterexamples are also given.

2010 Mathematics Subject Classification.   35B45, 47A55.

Key words and phrases.   Airy equation and operator, a priori estimates, relative boundedness, perturbation, self-adjoint operators.

DOI: 10.3336/gm.47.2.11

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