On the general form of linear functionals on the Hardy spaces \(H^1\) over compact abelian groups and some of its applications (Q2400624)
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| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the general form of linear functionals on the Hardy spaces \(H^1\) over compact abelian groups and some of its applications |
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On the general form of linear functionals on the Hardy spaces \(H^1\) over compact abelian groups and some of its applications (English)
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29 August 2017
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The celebrated Fefferman theorem on the general form of a linear functional on the Hardy space \(H^1\) is generalized to the case of an arbitrary compact abelian group with totally ordered dual. This leads to several corollaries that, in turn, can be applied to multiple lacunary Fourier series and to atomic characterization of the Hardy space on the two-dimensional torus.
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bounded mean oscillation
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dual space
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lacunary series
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totally ordered abelian group
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Hankel operator
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atom
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