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Singular convolution integrals with operator-valued kernel

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Abstract

We study operators \(f\mapsto Kf\) of the form \((Kf)(t)=\int_{{\bf R}^{n}} k(t-s)f(s) {\rm d}s\), where f is a vector-valued function and k an operator-valued singular kernel. Sufficient conditions for boundedness on L p-spaces of UMD-valued functions are given in terms of a Hörmander-type condition involving R-boundedness. The results cover large classes of kernels and also provide new proofs of recent operator-valued Fourier multiplier theorems. Moreover, they give new information about families of singular integral operators.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Helsinki, Gustaf Hällströmin katu 2b, 00014, Helsinki, Finland

    Tuomas Hytönen

  2. Mathematisches Institut I, Universität Karlsruhe, Englerstrasse 2, 76128, Karlsruhe, Germany

    Lutz Weis

Authors
  1. Tuomas Hytönen
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  2. Lutz Weis
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Correspondence to Tuomas Hytönen.

Additional information

Tuomas Hytönen was supported by the Marie Curie Fellowship of the European Union.

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Hytönen, T., Weis, L. Singular convolution integrals with operator-valued kernel. Math. Z. 255, 393–425 (2007). https://doi.org/10.1007/s00209-006-0043-x

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  • DOI: https://doi.org/10.1007/s00209-006-0043-x

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