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A \(q\)-atomic decomposition of weighted tent spaces on spaces of homogeneous type and its application. (English) Zbl 1460.42038

Summary: The theory of tent spaces on \(\mathbb{R}^n\) was introduced by R. R. Coifman et al. [Lect. Notes Math. 992, 1–15 (1983; Zbl 0523.42016), “Some new functions and their applications to harmonic analysis”, J. Funct. Anal. 62, 304–335 (1985)], including atomic decomposition, duality theory and so on. E. Russ [“The atomic decomposition for tent spaces on spaces of homogeneous type” (2006), https://maths.anu.edu.au/files/CMAProc42-r.pdf] generalized the atomic decomposition for tent spaces to the case of spaces of homogeneous type \((X,d,\mu)\). The main purpose of this paper is to extend the results of Coifman et al. [loc. cit.] and Russ [loc. cit.] to weighted version. More precisely, we obtain a \(q\)-atomic decomposition for the weighted tent spaces \(T^p_{2,w}(X)\), where \(0<p\leq 1\), \(1<q<\infty\), and \(w\in A_\infty\). As an application, we give an atomic decomposition for weighted Hardy spaces associated to non-negative self-adjoint operators on \(X\).

MSC:

42B35 Function spaces arising in harmonic analysis
42B30 \(H^p\)-spaces
47F05 General theory of partial differential operators
30H05 Spaces of bounded analytic functions of one complex variable

Citations:

Zbl 0523.42016
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References:

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