On \(g\)-functions for Laguerre function expansions of Hermite type (Q353969)
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scientific article; zbMATH DE number 6188680
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On \(g\)-functions for Laguerre function expansions of Hermite type |
scientific article; zbMATH DE number 6188680 |
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On \(g\)-functions for Laguerre function expansions of Hermite type (English)
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17 July 2013
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The paper contains a thorough analysis of square functions based on heat-diffusion and Poisson semigroups in the multi-dimensional framework of Laguerre expansions of Hermite type. It is proved that with a (natural) restriction on the type multi-index \(\alpha\), the considered square functions related to expansions with respect to the Laguerre system \(\{\varphi^\alpha_k\}\), \(k\in \mathbb N^d\), are vector-valued Calderón-Zygmund operators and thus their mapping \(L^p\) properties follow. Results proved in the present paper complete and improve a number of results obtained earlier by several authors.
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Laguerre function expansions of Hermite type
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square functions
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vector-valued Calderón-Zygmund operators
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0.9463445
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0.90536183
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0.9051529
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0.8954591
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0.89221984
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0.8888841
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0.8867241
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