Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 38, 2013, 209-227

MULTIPLIERS AND IMAGINARY POWERS OF THE SCHRÖDINGER OPERATORS CHARACTERIZING UMD BANACH SPACES

Jorge J. Betancor, Raquel Crescimbeni, Juan C. Fariña and Lourdes Rodríguez-Mesa

Universidad de la Laguna, Departamento de Análisis Matemático
Campus de Anchieta, Avda. Astrofísico Francisco Sánchez, s/n
38271 La Laguna, (Sta. Cruz de Tenerife), España; jbetanco 'at' ull.es

Universidad Nacional de Comahue, Departamento de Matemáticas
8300 Neuquén, Argentina; raquel.crescimbeni 'at' faea.uncoma.edu.ar

Universidad de la Laguna, Departamento de Análisis Matemático
Campus de Anchieta, Avda. Astrofísico Francisco Sánchez, s/n
38271 La Laguna, (Sta. Cruz de Tenerife), España; jcfarina 'at' ull.es

Universidad de la Laguna, Departamento de Análisis Matemático
Campus de Anchieta, Avda. Astrofísico Francisco Sánchez, s/n
38271 La Laguna, (Sta. Cruz de Tenerife), España; lrguez 'at' ull.es

Abstract. In this paper we establish L^p-boundedness properties for Laplace type transform spectral multipliers associated with the Schrödinger operator L = -\Delta + V. We obtain for this type of multipliers pointwise representation as principal value integral operators. We also characterize the UMD Banach spaces in terms of the L^p-boundedness of the imaginary powers L^i\gamma, \gamma \in R, of L.

2010 Mathematics Subject Classification: Primary 42C05; Secondary 42C15.

Key words: UMD spaces, Schrödinger operators, multipliers, imaginary powers.

Reference to this article: J.J. Betancor, R. Crescimbeni, J.C. Fariña and L. Rodríguez-Mesa: Multipliers and imaginary powers of the Schrödinger operators characterizing UMD Banach spaces. Ann. Acad. Sci. Fenn. Math. 38 (2013), 209-227.

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doi:10.5186/aasfm.2013.3813