Pointwise Multipliers of Zygmund Classes on'Equation missing'

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Autoři: Wen Yuan, Aline Bonami, Liguang Liu, Dachun Yang
Zdroj: The Journal of Geometric Analysis. 31:8879-8902
Informace o vydavateli: Springer Science and Business Media LLC, 2020.
Rok vydání: 2020
Témata: Pointwise, Pure mathematics, Dual space, 010102 general mathematics, Pointwise product, Hardy space, Space (mathematics), Lipschitz continuity, 01 natural sciences, symbols.namesake, Differential geometry, 0103 physical sciences, symbols, Standard probability space, 010307 mathematical physics, Geometry and Topology, 0101 mathematics, Mathematics
Popis: It is well known that Lipschitz spaces on the torus are an algebra. It is no more the case in the non compact situation because of the behavior at infinity. This is a companion article to Bonami et al. (J Math Pures Appl (9) 131:130–170, 2019), where pointwise multipliers on Lipschitz spaces on $${\mathbb {R}}^n$$ are characterized for non-integer values of the parameter. In this article, the authors first establish two equivalent characterizations of a modified Zygmund space, and then characterize the pointwise multipliers on Lipschitz spaces on $${\mathbb {R}}^n$$ for the integer values of the parameter, in particular, for the Zygmund class, via the intersection of the Lebesgue space $$L^\infty ({\mathbb {R}}^n)$$ and the modified Zygmund space. This result can be used to show that the bilinear decomposition of the pointwise product of the Hardy space and its dual, in the integer values of the parameter, obtained in the aforementioned reference is sharp in the dual space sense.
ISSN: 1559-002X
1050-6926
Přístupová URL adresa: https://explore.openaire.eu/search/publication?articleId=doi_________::4ec4e15d537056cf4aa8438ceb28cda6
https://doi.org/10.1007/s12220-020-00453-8
Rights: CLOSED
Přírůstkové číslo: edsair.doi...........4ec4e15d537056cf4aa8438ceb28cda6
Autor: Wen Yuan, Aline Bonami, Liguang Liu, Dachun Yang
Rok vydání: 2020
Předmět:
Zdroj: The Journal of Geometric Analysis. 31:8879-8902
ISSN: 1559-002X
1050-6926
Popis: It is well known that Lipschitz spaces on the torus are an algebra. It is no more the case in the non compact situation because of the behavior at infinity. This is a companion article to Bonami et al. (J Math Pures Appl (9) 131:130–170, 2019), where pointwise multipliers on Lipschitz spaces on $${\mathbb {R}}^n$$ are characterized for non-integer values of the parameter. In this article, the authors first establish two equivalent characterizations of a modified Zygmund space, and then characterize the pointwise multipliers on Lipschitz spaces on $${\mathbb {R}}^n$$ for the integer values of the parameter, in particular, for the Zygmund class, via the intersection of the Lebesgue space $$L^\infty ({\mathbb {R}}^n)$$ and the modified Zygmund space. This result can be used to show that the bilinear decomposition of the pointwise product of the Hardy space and its dual, in the integer values of the parameter, obtained in the aforementioned reference is sharp in the dual space sense.
Databáze: OpenAIRE
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