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Published in 2017 at "Journal of Fourier Analysis and Applications"
DOI: 10.1007/s00041-016-9499-1
Abstract: Harmonic Besov and Triebel–Lizorkin spaces on the unit ball in $${\mathbb R}^d$$Rd with full range of parameters are introduced and studied. It is shown that these spaces can be identified with respective Besov and Triebel–Lizorkin…
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Keywords:
lizorkin spaces;
harmonic besov;
triebel lizorkin;
besov triebel ... See more keywords
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1
Published in 2017 at "Journal of Fourier Analysis and Applications"
DOI: 10.1007/s00041-018-9617-3
Abstract: We discuss generalizations of Rubio de Francia’s inequality for Triebel–Lizorkin and Besov spaces, continuing the research from Osipov (Sb Math 205(7): 1004–1023, 2014) and answering Havin’s question to one of the authors. Two versions of…
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Keywords:
triebel lizorkin;
besov spaces;
lizorkin besov;
rubio francia ... See more keywords
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Published in 2019 at "Journal of Fourier Analysis and Applications"
DOI: 10.1007/s00041-021-09837-y
Abstract: We prove the continuous dependence of the solution maps for the Euler equations in the (critical) Triebel–Lizorkin spaces, which was not shown in the previous works [ 6 , 7 , 9 ]. The proof…
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Keywords:
triebel lizorkin;
posedness euler;
remarks well;
lizorkin spaces ... See more keywords
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Published in 2018 at "Acta Mathematica Sinica, English Series"
DOI: 10.1007/s10114-018-7311-7
Abstract: This article is devoted to the study of variable 2-microlocal Besov-type and Triebel–Lizorkin-type spaces. These variable function spaces are defined via a Fourier-analytical approach. The authors then characterize these spaces by means of ϕ-transforms, Peetre…
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Keywords:
type;
variable microlocal;
triebel lizorkin;
microlocal besov ... See more keywords
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Published in 2019 at "Positivity"
DOI: 10.1007/s11117-019-00650-y
Abstract: In this paper we define Lipschitz and Triebel–Lizorkin spaces associated with the differential-difference Dunkl operators on $$\mathbb {R}^d$$Rd. We study inclusion relations among them. Next, some interpolation results and continuity results of some important operators…
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Keywords:
lizorkin spaces;
triebel lizorkin;
dunkl;
lipschitz triebel ... See more keywords
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Published in 2020 at "Science China Mathematics"
DOI: 10.1007/s11425-017-9416-5
Abstract: In this paper, we systematically study several classes of maximal singular integrals and maximal functions with rough kernels in $$\mathscr{F}_{\beta}\left(\mathrm{S}^{n-1}\right)$$ ℱ β ( S n − 1 ) , a topic that relates to the…
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Keywords:
maximal functions;
triebel lizorkin;
boundedness continuity;
singular integrals ... See more keywords
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Published in 2019 at "Frontiers of Mathematics in China"
DOI: 10.1007/s11464-019-0742-3
Abstract: We establish the boundedness and continuity of parametric Marcinkiewicz integrals associated to homogeneous compound mappings on Triebel-Lizorkin spaces and Besov spaces. Here the integral kernels are provided with some rather weak size conditions on the…
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Keywords:
boundedness continuity;
mappings triebel;
marcinkiewicz integrals;
associated homogeneous ... See more keywords
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Published in 2019 at "Journal of Mathematical Analysis and Applications"
DOI: 10.1016/j.jmaa.2018.11.086
Abstract: In this paper, we investigate the relation between Sobolev-type embeddings of Haj{\l}asz-Besov spaces (and also Haj{\l}asz-Triebel-Lizorkin spaces) defined on a metric measure space $(X,d,\mu)$ and lower bound for the measure $\mu.$ We prove that if…
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Keywords:
asz triebel;
asz besov;
embeddings haj;
triebel lizorkin ... See more keywords
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Published in 2020 at "Journal of Mathematical Analysis and Applications"
DOI: 10.1016/j.jmaa.2019.123801
Abstract: Abstract In this note, we correct a technical error in the proof of Theorem 2.2 in [1] .
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Keywords:
triebel lizorkin;
type besov;
corrigendum characterizations;
morrey type ... See more keywords
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Published in 2017 at "Canadian Mathematical Bulletin"
DOI: 10.4153/cmb-2016-076-7
Abstract: Abstract Let $\ell \in \mathbb{N}$ and $\alpha \in (0,2\ell )$ . In this article, the authors establish equivalent characterizations of Besov-type spaces, Triebel–Lizorkin-type spaces, and Besov–Morrey spaces via the sequence ${{\{f-{{B}_{\ell ,{{2}^{-k}}}}f\}}_{k}}$ consisting of the…
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Keywords:
triebel lizorkin;
besov type;
characterizations besov;
type spaces ... See more keywords