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Boundedness of Some Paraproducts on Spaces of Homogeneous Type

Author

Listed:
  • Xing Fu

    (Hubei Key Laboratory of Applied Mathematics, Faculty of Mathematics and Statistics, Hubei University, Wuhan 430062, China)

Abstract

Let ( X , d , μ ) be a space of homogeneous type in the sense of Coifman and Weiss. In this article, the author develops a partial theory of paraproducts { Π j } j = 1 3 defined via approximations of the identity with exponential decay (and integration 1), which are extensions of paraproducts defined via regular wavelets. Precisely, the author first obtains the boundedness of Π 3 on Hardy spaces and then, via the methods of interpolation and the well-known T ( 1 ) theorem, establishes the endpoint estimates for { Π j } j = 1 3 . The main novelty of this paper is the application of the Abel summation formula to the establishment of some relations among the boundedness of { Π j } j = 1 3 , which has independent interests. It is also remarked that, throughout this article, μ is not assumed to satisfy the reverse doubling condition.

Suggested Citation

  • Xing Fu, 2021. "Boundedness of Some Paraproducts on Spaces of Homogeneous Type," Mathematics, MDPI, vol. 9(20), pages 1-26, October.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:20:p:2591-:d:656994
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    References listed on IDEAS

    as
    1. Yongsheng Han & Detlef Müller & Dachun Yang, 2008. "A Theory of Besov and Triebel-Lizorkin Spaces on Metric Measure Spaces Modeled on Carnot-Carathéodory Spaces," Abstract and Applied Analysis, Hindawi, vol. 2008, pages 1-250, March.
    2. Ziyi He & Dachun Yang & Wen Yuan, 2021. "Real‐variable characterizations of local Hardy spaces on spaces of homogeneous type," Mathematische Nachrichten, Wiley Blackwell, vol. 294(5), pages 900-955, May.
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    2. Ziyi He & Dachun Yang & Wen Yuan, 2021. "Real‐variable characterizations of local Hardy spaces on spaces of homogeneous type," Mathematische Nachrichten, Wiley Blackwell, vol. 294(5), pages 900-955, May.

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