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Riesz transformations of distributions and a generalized Hardy space

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Approximation Theory and its Applications

Abstract

LeiE(ℝn) be the space of all functions on ℝn which can continue to the entire holomorphic functions on ℂn. We define Riesz transformation Rj of distributions as a linear transformation of the quotient spaceD′(ℝn)/E(ℝn) to itself, j=1,2,..., n. These generalized Riesz transformations share the same properties with the classical ones, such as\(\sum\limits_{j = 1}^n {R_j^2 } = - I\). As applications we generalize further a theorem of F. & M. Riesz generalized by Stein and Weiss, and then define a generalized Hardy space, of which some properties are studied.

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Authors and Affiliations

  1. Institute of System Science, Academia Sinica, China

    Li Banghe & Guo Likang

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  1. Li Banghe
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  2. Guo Likang
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Banghe, L., Likang, G. Riesz transformations of distributions and a generalized Hardy space. Approx. Theory & its Appl. 5, 1–17 (1989). https://doi.org/10.1007/BF02836065

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  • DOI: https://doi.org/10.1007/BF02836065

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