Fourier multiplier theorems for Triebel–Lizorkin spaces

Bae Jun Park

doi:10.1007/s00209-018-2180-4

Fourier multiplier theorems for Triebel–Lizorkin spaces

Bae Jun Park

Korea Institute for Advanced Study

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

In this paper we study sharp generalizations of F˙p0,q multiplier theorem of Mikhlin–Hörmander type. The class of multipliers that we consider involves Herz spaces Kus,t. Plancherel’s theorem proves Ls2^=K2s,2 and we study the optimal triple (u, t, s) for which supk∈Z‖(m(2k·)φ)∨‖Kus,t<∞ implies F˙p0,q boundedness of multiplier operator T_m where φ is a cutoff function. Our result also covers the BMO-type space F˙∞0,q.

Original language	English
Pages (from-to)	221-258
Number of pages	38
Journal	Mathematische Zeitschrift
Volume	293
Issue number	1-2
DOIs	https://doi.org/10.1007/s00209-018-2180-4
State	Published - 1 Oct 2019
Externally published	Yes

Keywords

Fourier multipliers
Hörmander–Mikhlin multipliers
Triebel–Lizorkin spaces

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10.1007/s00209-018-2180-4

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title = "Fourier multiplier theorems for Triebel–Lizorkin spaces",

abstract = "In this paper we study sharp generalizations of F˙p0,q multiplier theorem of Mikhlin–H{\"o}rmander type. The class of multipliers that we consider involves Herz spaces Kus,t. Plancherel{\textquoteright}s theorem proves Ls2\textasciicircum{}=K2s,2 and we study the optimal triple (u, t, s) for which supk∈Z‖(m(2k·)φ)∨‖Kus,t<∞ implies F˙p0,q boundedness of multiplier operator Tm where φ is a cutoff function. Our result also covers the BMO-type space F˙∞0,q.",

keywords = "Fourier multipliers, H{\"o}rmander–Mikhlin multipliers, Triebel–Lizorkin spaces",

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note = "Publisher Copyright: {\textcopyright} 2018, Springer-Verlag GmbH Germany, part of Springer Nature.",

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AU - Park, Bae Jun

PY - 2019/10/1

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N2 - In this paper we study sharp generalizations of F˙p0,q multiplier theorem of Mikhlin–Hörmander type. The class of multipliers that we consider involves Herz spaces Kus,t. Plancherel’s theorem proves Ls2^=K2s,2 and we study the optimal triple (u, t, s) for which supk∈Z‖(m(2k·)φ)∨‖Kus,t<∞ implies F˙p0,q boundedness of multiplier operator Tm where φ is a cutoff function. Our result also covers the BMO-type space F˙∞0,q.

AB - In this paper we study sharp generalizations of F˙p0,q multiplier theorem of Mikhlin–Hörmander type. The class of multipliers that we consider involves Herz spaces Kus,t. Plancherel’s theorem proves Ls2^=K2s,2 and we study the optimal triple (u, t, s) for which supk∈Z‖(m(2k·)φ)∨‖Kus,t<∞ implies F˙p0,q boundedness of multiplier operator Tm where φ is a cutoff function. Our result also covers the BMO-type space F˙∞0,q.

KW - Fourier multipliers

KW - Hörmander–Mikhlin multipliers

KW - Triebel–Lizorkin spaces

UR - https://www.scopus.com/pages/publications/85056482352

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DO - 10.1007/s00209-018-2180-4

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VL - 293

SP - 221

EP - 258

JO - Mathematische Zeitschrift

JF - Mathematische Zeitschrift

IS - 1-2

ER -

Fourier multiplier theorems for Triebel–Lizorkin spaces

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