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Keywords = paraproduct

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26 pages, 427 KiB  
Article
Boundedness of Some Paraproducts on Spaces of Homogeneous Type
by Xing Fu
Mathematics 2021, 9(20), 2591; https://doi.org/10.3390/math9202591 - 15 Oct 2021
Viewed by 1596
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 {Πj}j=13 defined via approximations [...] Read more.
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 {Πj}j=13 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 Π3 on Hardy spaces and then, via the methods of interpolation and the well-known T(1) theorem, establishes the endpoint estimates for {Πj}j=13. The main novelty of this paper is the application of the Abel summation formula to the establishment of some relations among the boundedness of {Πj}j=13, which has independent interests. It is also remarked that, throughout this article, μ is not assumed to satisfy the reverse doubling condition. Full article
(This article belongs to the Special Issue Recent Developments of Function Spaces and Their Applications I)
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