Haar bases on quasi-metric measure spaces, and dyadic structure theorems for function spaces on product spaces of homogeneous type. (English) Zbl 1347.42040
This paper has three main components:
(1) the explicit construction of a Haar basis for \(L^p\) associated to a system of dyadic cubes on a geometrically doubling quasi-metric space equipped with a positive Borel measure,
(2) the definition of dyadic product function spaces, by means of this Haar basis, on product spaces of homogeneuos type in the sense of Coifman and Weiss, and
(3) dyadic structure theorems relating the continuous and dyadic versions of these function spaces on product spaces of homogeneous type.
(1) the explicit construction of a Haar basis for \(L^p\) associated to a system of dyadic cubes on a geometrically doubling quasi-metric space equipped with a positive Borel measure,
(2) the definition of dyadic product function spaces, by means of this Haar basis, on product spaces of homogeneuos type in the sense of Coifman and Weiss, and
(3) dyadic structure theorems relating the continuous and dyadic versions of these function spaces on product spaces of homogeneous type.
Reviewer: Koichi Saka (Akita)
MSC:
| 42B35 | Function spaces arising in harmonic analysis |
| 42B30 | \(H^p\)-spaces |
| 42B25 | Maximal functions, Littlewood-Paley theory |
| 42C40 | Nontrigonometric harmonic analysis involving wavelets and other special systems |
| 30L99 | Analysis on metric spaces |
Keywords:
Haar bases; quasi-metric measure spaces; dyadic product function spaces; spaces of homogeneous type; dyadic structure theorems; BMO space; Hardy space; doubling weights; Muckenhoupt \(A_{p}\) weights; reverse Hölder weights; maximal functionReferences:
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