Fourier Multipliers on Anisotropic Mixed-Norm Spaces of Distributions

Research output: Contribution to journalJournal articleResearchpeer-review

Abstract

A new general Hormander type condition involving anisotropies and mixed norms is introduced, and boundedness results for Fourier multi- pliers on anisotropic Besov and Triebel-Lizorkin spaces of distributions with mixed Lebesgue norms are obtained. As an application, the continuity of such operators is established on mixed Sobolev and Lebesgue spaces too. Some lifting properties and equivalent norms are obtained as well.
Original languageEnglish
JournalMathematica Scandinavica
Number of pages13
ISSN0025-5521
Publication statusAccepted/In press - 2019

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Mixed Norm Space
Fourier multipliers
Equivalent Norm
Norm
Triebel-Lizorkin Space
Lebesgue Space
Henri Léon Lebésgue
Sobolev Spaces
Anisotropy
Boundedness
Operator

Cite this

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title = "Fourier Multipliers on Anisotropic Mixed-Norm Spaces of Distributions",
abstract = "A new general Hormander type condition involving anisotropies and mixed norms is introduced, and boundedness results for Fourier multi- pliers on anisotropic Besov and Triebel-Lizorkin spaces of distributions with mixed Lebesgue norms are obtained. As an application, the continuity of such operators is established on mixed Sobolev and Lebesgue spaces too. Some lifting properties and equivalent norms are obtained as well.",
author = "Galatia Cleanthous and Athanasios Georgiadis and Morten Nielsen",
year = "2019",
language = "English",
journal = "Mathematica Scandinavica",
issn = "0025-5521",
publisher = "Aarhus Universitet * Mathematica Scandinavica",

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Fourier Multipliers on Anisotropic Mixed-Norm Spaces of Distributions. / Cleanthous, Galatia; Georgiadis, Athanasios; Nielsen, Morten.

In: Mathematica Scandinavica, 2019.

Research output: Contribution to journalJournal articleResearchpeer-review

TY - JOUR

T1 - Fourier Multipliers on Anisotropic Mixed-Norm Spaces of Distributions

AU - Cleanthous, Galatia

AU - Georgiadis, Athanasios

AU - Nielsen, Morten

PY - 2019

Y1 - 2019

N2 - A new general Hormander type condition involving anisotropies and mixed norms is introduced, and boundedness results for Fourier multi- pliers on anisotropic Besov and Triebel-Lizorkin spaces of distributions with mixed Lebesgue norms are obtained. As an application, the continuity of such operators is established on mixed Sobolev and Lebesgue spaces too. Some lifting properties and equivalent norms are obtained as well.

AB - A new general Hormander type condition involving anisotropies and mixed norms is introduced, and boundedness results for Fourier multi- pliers on anisotropic Besov and Triebel-Lizorkin spaces of distributions with mixed Lebesgue norms are obtained. As an application, the continuity of such operators is established on mixed Sobolev and Lebesgue spaces too. Some lifting properties and equivalent norms are obtained as well.

M3 - Journal article

JO - Mathematica Scandinavica

JF - Mathematica Scandinavica

SN - 0025-5521

ER -