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Weighted inequalities and a.e. convergence for Poisson integrals in light-cones

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Abstract

We show that the Poisson maximal operator for the tube over the light-cone, P *, is bounded in the weighted space L p(w) if and only if the weight w(x) belongs to the Muckenhoupt class A p . We also characterize with a geometric condition related to the intrinsic geometry of the cone the weights v(x) for which P * is bounded from L p(v) into L p(u), for some other weight u(x) > 0. Some applications to a.e. restricted convergence of Poisson integrals are given.

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Authors and Affiliations

  1. Institute of Mathematics, University of Wrocław, Pl. Grunwaldzki 2/4, 50-384, Wrocław, Poland

    E. Damek

  2. Department of Matemáticas C-XV, Universidad Autónoma de Madrid, 28049, Madrid, Spain

    G. Garrigós & J. L. Torrea

  3. Facultad Ingenierí a Química, Universidad Nacional de Litoral, Güemes 3450, 3000, Santa Fe, Argentina

    E. Harboure

Authors
  1. E. Damek
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  2. G. Garrigós
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  3. E. Harboure
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  4. J. L. Torrea
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Correspondence to E. Damek or J. L. Torrea.

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Damek, E., Garrigós, G., Harboure, E. et al. Weighted inequalities and a.e. convergence for Poisson integrals in light-cones. Math. Ann. 336, 727–746 (2006). https://doi.org/10.1007/s00208-006-0023-9

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  • DOI: https://doi.org/10.1007/s00208-006-0023-9

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