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A multiplier inclusion theorem on product domains

Part of: Harmonic analysis in several variables

Published online by Cambridge University Press:  20 June 2019

Odysseas Bakas
Odysseas Bakas*
Affiliation:
Department of Mathematics, Stockholm University, 106 91 Stockholm, Sweden ([email protected])
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Abstract

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In this note it is shown that the class of all multipliers from the d-parameter Hardy space $H_{{\rm prod}}^1 ({\open T}^d)$ to L2 (𝕋d) is properly contained in the class of all multipliers from L logd/2L (𝕋d) to L2(𝕋d).

Keywords

multiplier inclusionproduct Hardy spaceshigher-dimensional Zygmund inequalityLittlewood–Paley square function

MSC classification

Primary: 42B15: Multipliers
Secondary: 42B25: Maximal functions, Littlewood-Paley theory
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 62 , Issue 4 , November 2019 , pp. 1073 - 1088
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
Copyright © Edinburgh Mathematical Society 2019

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