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Commutators of Riesz Transforms Related to Schrödinger Operators

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Abstract

In this work we obtain boundedness on L p, for 1<p<∞, of commutators T b f=bTf−T(bf) where T is any of the Riesz transforms or their conjugates associated to the Schrödinger operator −Δ+V with V satisfying an appropriate reverse Hölder inequality. The class where b belongs is larger than the usual BMO. We also obtain a substitute result for p=∞, under a slightly stronger condition on b.

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Authors and Affiliations

  1. Instituto de Matemática Aplicada del Litoral CONICET-UNL, Santa Fe, Argentina

    B. Bongioanni, E. Harboure & O. Salinas

Authors
  1. B. Bongioanni
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  2. E. Harboure
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  3. O. Salinas
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Corresponding author

Correspondence to B. Bongioanni.

Additional information

Communicated by Fernando Soria.

This research is partially supported by Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET) and Universidad Nacional del Litoral (UNL), Argentina.

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Bongioanni, B., Harboure, E. & Salinas, O. Commutators of Riesz Transforms Related to Schrödinger Operators. J Fourier Anal Appl 17, 115–134 (2011). https://doi.org/10.1007/s00041-010-9133-6

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  • DOI: https://doi.org/10.1007/s00041-010-9133-6

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