Abstract
We extend some results of C. Demeter about the boundedness of series of difference of convolutions to the setting of one-sided A p weights. We need to use a different approach. To be precise, we prove that the kernel of the associated operator satisfies a generalized Hörmander condition. The weighted inequalities allow us to transfer the result to the ergodic case, when the operator is induced by a mean bounded, invertible, positive groups.
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The authors were supported by MEC Grant MTM2005-08350-C03-02 and Junta de Andalucía Grant FQM354.
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Lorente, M., de la Torre, A. Weighted and Ergodic Theorems for Series of Differences of Convolutions. J Fourier Anal Appl 14, 39–59 (2008). https://doi.org/10.1007/s00041-007-9005-x
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DOI: https://doi.org/10.1007/s00041-007-9005-x