Molecular decomposition and Fourier multipliers for holomorphic Besov and Triebel–Lizorkin spaces

Research output: Contribution to journalJournal articleResearchpeer-review

Abstract

Smooth molecular decompositions for holomorphic Besov and Triebel–Lizorkin spaces on the unit disk of the complex plane are constructed. The decompositions are used to obtain a boundedness result for Fourier multipliers. As further applications, we provide equivalent norms for the spaces under consideration, we consider the implications of the results on Hardy and Hardy–Sobolev spaces, and we study boundedness of coefficient multipliers.
Original languageEnglish
JournalMonatshefte für Mathematik
Volume188
Issue number3
Pages (from-to)467-493
Number of pages27
ISSN0026-9255
DOIs
Publication statusPublished - 11 Mar 2019

Fingerprint

Fourier multipliers
Triebel-Lizorkin Space
Besov Spaces
Boundedness
Equivalent Norm
Decompose
Argand diagram
Unit Disk
Multiplier
Coefficient

Keywords

  • Besov spaces
  • Distributions
  • Fourier multipliers
  • Hardy spaces
  • Hardy–Sobolev spaces
  • Holomorphic functions
  • Molecular decomposition
  • Triebel–Lizorkin spaces

Cite this

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title = "Molecular decomposition and Fourier multipliers for holomorphic Besov and Triebel–Lizorkin spaces",
abstract = "Smooth molecular decompositions for holomorphic Besov and Triebel–Lizorkin spaces on the unit disk of the complex plane are constructed. The decompositions are used to obtain a boundedness result for Fourier multipliers. As further applications, we provide equivalent norms for the spaces under consideration, we consider the implications of the results on Hardy and Hardy–Sobolev spaces, and we study boundedness of coefficient multipliers.",
keywords = "Besov spaces, Distributions, Fourier multipliers, Hardy spaces, Hardy–Sobolev spaces, Holomorphic functions, Molecular decomposition, Triebel–Lizorkin spaces",
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Molecular decomposition and Fourier multipliers for holomorphic Besov and Triebel–Lizorkin spaces. / Cleanthous, G.; Georgiadis, A. G.; Nielsen, M.

In: Monatshefte für Mathematik, Vol. 188, No. 3, 11.03.2019, p. 467-493.

Research output: Contribution to journalJournal articleResearchpeer-review

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T1 - Molecular decomposition and Fourier multipliers for holomorphic Besov and Triebel–Lizorkin spaces

AU - Cleanthous, G.

AU - Georgiadis, A. G.

AU - Nielsen, M.

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N2 - Smooth molecular decompositions for holomorphic Besov and Triebel–Lizorkin spaces on the unit disk of the complex plane are constructed. The decompositions are used to obtain a boundedness result for Fourier multipliers. As further applications, we provide equivalent norms for the spaces under consideration, we consider the implications of the results on Hardy and Hardy–Sobolev spaces, and we study boundedness of coefficient multipliers.

AB - Smooth molecular decompositions for holomorphic Besov and Triebel–Lizorkin spaces on the unit disk of the complex plane are constructed. The decompositions are used to obtain a boundedness result for Fourier multipliers. As further applications, we provide equivalent norms for the spaces under consideration, we consider the implications of the results on Hardy and Hardy–Sobolev spaces, and we study boundedness of coefficient multipliers.

KW - Besov spaces

KW - Distributions

KW - Fourier multipliers

KW - Hardy spaces

KW - Hardy–Sobolev spaces

KW - Holomorphic functions

KW - Molecular decomposition

KW - Triebel–Lizorkin spaces

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U2 - 10.1007/s00605-018-1251-2

DO - 10.1007/s00605-018-1251-2

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SP - 467

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JO - Monatshefte für Mathematik

JF - Monatshefte für Mathematik

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