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New Wavelet Bases and Isometric Between Symbolic Operators Spaces \( {\text{OP}}S^{m}_{{1,\delta }} \) and Kernel Distributions Spaces

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Abstract

In the fifties, Calderón established a formal relation between symbol and kernel distribution, but it is difficult to establish an intrinsic relation. The Calderón-Zygmund (C-Z) school studied the C-Z operators, and Hörmander, Kohn and Nirenberg, et al. studied the symbolic operators. Here we apply a refinement of the Littlewood-Paley (L-P) decomposition, analyse under new wavelet bases, to characterize both symbolic operators spaces \( {\text{OP}}S^{m}_{{1,\delta }} \) and kernel distributions spaces with other spaces composed of some almost diagonal matrices, then get an isometric between \( {\text{OP}}S^{m}_{{1,\delta }} \) and kernel distribution spaces

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Authors and Affiliations

  1. Department of Mathematics, Wuhan University, 430072, Hubei, P. R. China

    Qi Xiang Yang

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  1. Qi Xiang Yang
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Correspondence to Qi Xiang Yang.

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Supported by a foundation from the Education Ministry of China for young scholars back from abroad

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Yang, Q.X. New Wavelet Bases and Isometric Between Symbolic Operators Spaces \( {\text{OP}}S^{m}_{{1,\delta }} \) and Kernel Distributions Spaces. Acta Math Sinica 18, 107–118 (2002). https://doi.org/10.1007/s101140000082

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  • DOI: https://doi.org/10.1007/s101140000082

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