Adaptive deterministic dyadic grids on spaces of homogeneous type (Q2926667)
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scientific article; zbMATH DE number 6363762
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Adaptive deterministic dyadic grids on spaces of homogeneous type |
scientific article; zbMATH DE number 6363762 |
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3 November 2014
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space of homogeneous type
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vector-valued space
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UMD-space
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adaptive dyadic grid
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rearrangement operator
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stripe operator
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martingale difference sequence
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vector-valued \(T(1)\) theorem
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Adaptive deterministic dyadic grids on spaces of homogeneous type (English)
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The authors develop a method to construct dyadic grids which are adapted deterministically to a given combinatorial situation on a space of homogeneous type.NEWLINENEWLINEThis allows them to simplify the hard combinatorial arguments for the estimation of the rearrangement operators used in the proof of the vector-valued \(T(1)\) theorem on spaces of homogeneous type by \textit{P. F. X. Müller} and \textit{M. Passenbrunner} [J. Funct. Anal. 262, No. 4, 1427--1465 (2012; Zbl 1241.42013)].NEWLINENEWLINEThe authors also apply the method to generalize the vector-valued results of \textit{R. Lechner} [Diss. Math. 503 (2014; Zbl 1321.46042)] on stripe operators to spaces of homogeneous type.
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