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A characterization of Lp(ℝ) by local trigonometric bases with 1<p<∞

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Abstract

We show that the local trigonometric bases introduced by Malvar, Coifman and Meyer constitute bases, but not unconditional bases, for Lp(ℝ) with 1<p<∞, p≠2. In addition, we characterize the functions in Lp(ℝ) for 1<p<∞ in terms of their local trigonometric basis coefficients.

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Authors and Affiliations

  1. Department of Mathematics, Beijing Jiaotong University, Beijing, 100044, P. R. China

    Qiaofang Lian & Yongge Wang

  2. Department of Applied Mathematics, Beijing University of Aeronautics and Astronautics, Beijing, 100083, P. R. China

    Yongge Wang

  3. School of Information Science and Engineering, the Graduate School of the Chinese Academy of Sciences, Beijing, 100039, P. R. China

    Dunyan Yan

Authors
  1. Qiaofang Lian
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  2. Yongge Wang
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  3. Dunyan Yan
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Additional information

Communicated by A. Zhou

Dedicated to Dr. Charles A. Micchelli for his 60th birthday

Mathematics subject classification (2000)

42C15.

Supported by Prof. Y. Xu under his grant in program of “One Hundred Distinguished Chinese Scientists” of the Chinese Academy of Sciences, the National Natural Science Foundation of China (No. 10371122), and the second author is supported by Tianyuan Fund for Mathematics (No. A0324648).

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Lian, Q., Wang, Y. & Yan, D. A characterization of Lp(ℝ) by local trigonometric bases with 1<p<∞. Adv Comput Math 25, 91–104 (2006). https://doi.org/10.1007/s10444-004-7625-0

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  • DOI: https://doi.org/10.1007/s10444-004-7625-0

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