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An oscillating multiplier on Herz type spaces

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Abstract

In this paper, the boundedness of an oscillating multiplier m γ,β for different β on the Herz type spaces is obtained. This operator was initially studied by Wainger and Fefferman-Stein. Our results extend one of the main results in a paper by **aochun Li and Shanzhen Lu for the non-weighted case, if β is close to 1 or α is suitably large. For β ≥ 1, the results with no weights on the Herz type spaces are also new.

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Authors and Affiliations

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

    Wei Cao

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

    Li-**g Sun

Authors
  1. Wei Cao
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  2. Li-**g Sun
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Corresponding author

Correspondence to Wei Cao.

Additional information

Supported by the National Natural Science Foundation of China (10931001, 10871173).

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Cao, W., Sun, Lj. An oscillating multiplier on Herz type spaces. Appl. Math. J. Chin. Univ. 26, 93–103 (2011). https://doi.org/10.1007/s11766-011-2425-z

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  • DOI: https://doi.org/10.1007/s11766-011-2425-z

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