Boundedness of Some Paraproducts on Spaces of Homogeneous Type

Xing Fu
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Xing Fu: Hubei Key Laboratory of Applied Mathematics, Faculty of Mathematics and Statistics, Hubei University, Wuhan 430062, China

Mathematics, 2021, vol. 9, issue 20, 1-26

Abstract: Let ( X , d , ? ) be a space of homogeneous type in the sense of Coifman and Weiss. In this article, the author develops a partial theory of paraproducts { ? 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 ? 3 on Hardy spaces and then, via the methods of interpolation and the well-known T ( 1 ) theorem, establishes the endpoint estimates for { ? 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 { ? j } j = 1 3 , which has independent interests. It is also remarked that, throughout this article, ? is not assumed to satisfy the reverse doubling condition.

Keywords: space of homogeneous type; paraproduct; T (1) theorem; hardy space; bilinear estimate (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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