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L p-boundedness properties of variation operators in the Schrödinger setting

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Abstract

In this paper we establish the L p-boundedness properties of the variation operators associated with the heat semigroup, Riesz transforms and commutator between Riesz transforms and multiplication by BMO(ℝn)-functions in the Schrödinger setting.

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Acknowledgements

The authors would like to thank the referee for pointing out the results in the recent paper [20] and his valuable comments that allow us to improve this paper.

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Authors and Affiliations

  1. Departamento de Análisis Matemático, Universidad de la Laguna, Campus de Anchieta, Avda. Astrofísico Francisco Sánchez, s/n, 38271, La Laguna (Sta. Cruz de Tenerife), Spain

    J. J. Betancor, J. C. Fariña & L. Rodríguez-Mesa

  2. Instituto de Matemática Aplicada del Litoral, IMAL, Universidad Nacional del Litoral, C/Gëmes, Santa Fe, Argentina

    E. Harboure

Authors
  1. J. J. Betancor
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  2. J. C. Fariña
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  3. E. Harboure
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  4. L. Rodríguez-Mesa
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Corresponding author

Correspondence to J. C. Fariña.

Additional information

This paper is partially supported by MTM2007/65609 and MTM2010/17974 (Spain) and by Consejo Nacional de Investigaciones Científicas y Técnicas (Argentina), PIP 2303.

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Betancor, J.J., Fariña, J.C., Harboure, E. et al. L p-boundedness properties of variation operators in the Schrödinger setting. Rev Mat Complut 26, 485–534 (2013). https://doi.org/10.1007/s13163-012-0094-y

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  • DOI: https://doi.org/10.1007/s13163-012-0094-y

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