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Boundedness of an oscillating multiplier on Triebel-Lizorkin spaces

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Abstract

In this paper, we study Triebel-Lizorkin space estimates for an oscillating multiplier m Ω,α,β . This operator was initially studied by Wainger and by Fefferman-Stein in the Lebesgue spaces. We obtain the boundedness results on the Triebel-Lizorkin space Ḟ α,q p (ℝn) for different p, q.

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Authors and Affiliations

  1. Department of Mathematics, Zhejiang University, Hangzhou, 310027, P. R. China

    Wei Cao & Jie Cheng Chen

  2. Department of Mathematics, University of Wisconsin-Milwaukee, Milwaukee, WI, 53217, USA

    Da Shan Fan

Authors
  1. Wei Cao
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  2. Jie Cheng Chen
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  3. Da Shan Fan
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Correspondence to Wei Cao.

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Supported by National Natural Science Foundation of China (Grant Nos. 10931001 and 10871173)

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Cao, W., Chen, J.C. & Fan, D.S. Boundedness of an oscillating multiplier on Triebel-Lizorkin spaces. Acta. Math. Sin.-English Ser. 26, 2071–2084 (2010). https://doi.org/10.1007/s10114-010-9573-6

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  • DOI: https://doi.org/10.1007/s10114-010-9573-6

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