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On oscillating kernels in the Besov space

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Approximation Theory and its Applications

Abstract

In this paper we consider a convolution operator Tf=p.v. Ω * f with Ω(x)=K(x)×eiλh(x), λ>0, where K(x) is a weak Calderón-Zygmund kernel and h(x) is a real-valued differentiable function. We give a boundedness criterion for such an operator to map the Besov space B 0.11 (Rn) into itself.

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Authors and Affiliations

  1. Department of Mathematical Sciences, University of Wisconsin-Milwaukee, 53201, Milwaukee, Wisconsin, USA

    Dashan Fan

  2. Department of Mathematics, Beijing Normal University, 100875, Beijing, The People's Republic of China

    Dachun Yang

Authors
  1. Dashan Fan
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  2. Dachun Yang
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Corresponding author

Correspondence to Dashan Fan.

Additional information

This research was partially supported by NNSF and NEC in P. R. China.

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Fan, D., Yang, D. On oscillating kernels in the Besov space. Approx. Theory & its Appl. 14, 32–45 (1998). https://doi.org/10.1007/BF02856147

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  • DOI: https://doi.org/10.1007/BF02856147

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