Mikhlin-Type Hp Multiplier Theorem on the Heisenberg Group

The classical Fourier multiplier theorem by Mikhlin in Hardy spaces is extended to the Heisenberg group. The proof relies on the theories of atom and molecule functions and the property of special Hermite functions. The main result is a Mikhlin-type Hp multiplier theorem on the Heisenberg group. If...

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Bibliographic Details
Published in:Axioms 2024-11, Vol.13 (11), p.745
Main Authors: Xiao, Jinsen, He, Jianxun, Wu, Yingzhu
Format: Article
Language:English
Subjects:
Fourier transform
Fourier transforms
Functional equations
Functions
Hardy space
Harmonic analysis
Heisenberg group
Lie groups
multiplier
Multipliers
Operators (mathematics)
Theorems
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Summary:The classical Fourier multiplier theorem by Mikhlin in Hardy spaces is extended to the Heisenberg group. The proof relies on the theories of atom and molecule functions and the property of special Hermite functions. The main result is a Mikhlin-type Hp multiplier theorem on the Heisenberg group. If an operator-valued function M(λ) satisfies certain conditions, the right-multiplier operator TM is bounded on the Hardy space Hp(Hn), which is defined in terms of maximal functions, and elements can be decomposed into atoms or molecules. The paper also discusses the relationship with other results and open problems.
ISSN:2075-1680
2075-1680
DOI:10.3390/axioms13110745