Inclusion relations between modulation and Triebel-Lizorkin spaces

Guo, Weichao; Wu, Huoxiong; Zhao, Guoping

doi:10.1090/proc/13614

Cited by 11 publications

(6 citation statements)

References 25 publications

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“…• s 2 if and only if the indices' relations in (26) are satisfied, cf. for instance [23,Lemma 2.10]. This concludes the proof.…”

Section: Function Spaces and Preliminariessupporting

confidence: 62%

“…Several authors have studied inclusion relations of such spaces with other classical function spaces such as Besov, Triebel-Lizorkin Gelfand-Shilov spaces [23,31,35,40]. In particular, when they are considered as symbol classes for pseudodifferential or Fourier integral operators, their relationship with classical symbol spaces such as the Hörmander classes or the Shubin-Sobolev spaces has been investigated in many contributions (see e.g., [4,10,25,36] and the references therein).…”

Section: Introduction and Resultsmentioning

confidence: 99%

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Characterization of smooth symbol classes by Gabor matrix decay

Bastianoni¹,

Cordero²

2021

Preprint

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For m ∈ R we introduce the symbol classes S m , m ∈ R, consisting of smooth functions σ on R 2d such that, and we show that can be characterized by an intersection of different types of modulation spaces. In the case m = 0 we recapture the Hörmander class S 0 0,0 that can be obtained by intersection of suitable Besov spaces as well. Such spaces contain the Shubin classes Γ m ρ , 0 < ρ ≤ 1, and can be viewed as their limit case ρ = 0. We exhibit almost diagonalization properties for the Gabor matrix of τ -pseudodifferential operators with symbols in such classes, extending the characterization proved by Gröchenig and Rzeszotnik in [22]. Finally, we compute the Gabor matrix of a Born-Jordan operator, which allows to prove new boundedness results for such operators.

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“…• s 2 if and only if the indices' relations in (26) are satisfied, cf. for instance [23,Lemma 2.10]. This concludes the proof.…”

Section: Function Spaces and Preliminariessupporting

confidence: 62%

Section: Introduction and Resultsmentioning

confidence: 99%

Characterization of smooth symbol classes by Gabor matrix decay

Bastianoni¹,

Cordero²

2021

Preprint

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“…We refer the reader to [5] for some motivations and historical remarks. One can also refer our recent paper [8,9] for the properties of modulation spaces and Wiener amalgam spaces.…”

Section: Introduction and Preliminarymentioning

confidence: 99%

Hausdorff operators on modulation and Wiener amalgam spaces

Zhao¹,

Fan²,

Guo³

2018

Ann. Funct. Anal.

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“…We refer the reader to [15] for some motivations and historical remarks. One is also referred to our recent papers [16][17][18] for the properties of modulation spaces.…”

Section: Introduction and Preliminarymentioning

confidence: 99%