Two new BMO spaces and sharp operators for \(B\)-valued martingales (Q2719631)
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scientific article; zbMATH DE number 1609831
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Two new BMO spaces and sharp operators for \(B\)-valued martingales |
scientific article; zbMATH DE number 1609831 |
Statements
25 June 2001
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Banach space-valued martingale
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BMO space
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sharp operator
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0.8908918
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0.8788089
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0.87596244
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0.87238705
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Two new BMO spaces and sharp operators for \(B\)-valued martingales (English)
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On a Banach space \(X\), two new BMO spaces \(\text{BMO}_{r}^{\sigma(p)}(X)\) and \(\text{BMO}_{r}^{S(p)}(X)\) are introduced. With two sharp operators \(f_{r}^{S(p)}\) and \(f_{r}^{\sigma(p)}\), generated by the conditional \(p\)-mean-square and \(p\)-mean-square operator, respectively, the author investigates the connection between \(\text{BMO}_{p}^{\sigma(p)}(X)\) and \(\text{BMO}_{p}^{+}\), \(\text{BMO}_{p}^{S(p)}(X)\) and \(\text{BMO}_{p}\). This result delivers a characterization of the convexity and smoothness of Banach space.
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