Lebesgue Points of Besov and Triebel–Lizorkin Spaces with Generalized Smoothness
Mathematics, 2021 In this article, the authors study the Lebesgue point of functions from Hajłasz–Sobolev, Besov, and Triebel–Lizorkin spaces with generalized smoothness on doubling metric measure spaces and prove that the exceptional sets of their Lebesgue points have ...
Ziwei Li, Dachun Yang, Wen Yuan
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Local Characterizations of Besov and Triebel-Lizorkin Spaces with Variable Exponent
Journal of Function Spaces, 2014 We introduce new Besov and Triebel-Lizorkin spaces with variable integrable exponent, which are different from those introduced by the second author early.
Baohua Dong, Jingshi Xu
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Boundedness of Generalized Parametric Marcinkiewicz Integrals Associated to Surfaces
Mathematics, 2019 In this article, the boundedness of the generalized parametric Marcinkiewicz integral operators M Ω , ϕ , h , ρ ( r ) is considered. Under the condition that Ω is a function in L q ( S n - 1 ) with q &
Mohammed Ali, Oqlah Al-Refai
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Continuous Characterizations of Besov-Lizorkin-Triebel Spaces and New Interpretations as Coorbits
Journal of Function Spaces and Applications, 2012 We give characterizations for homogeneous and inhomogeneous Besov-Lizorkin-Triebel spaces (H. Triebel 1983, 1992, and 2006) in terms of continuous local means for the full range of parameters.
Tino Ullrich
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Some of integral operators on space of Triebel-Lizorkin(Triebel-Lizorkin空间上的一类积分算子)
Zhejiang Daxue xuebao. Lixue ban, 2004 主要讨论了由分数次积分算子，奇异积分算子及Lipschiz函数所构成的几类Toeplitz型算子是Lp 到有界的， ，其中，从而的Lp到有界性，包括了当交换子TA是Lp到有界性及是Lp到有界性，.
WANGLei(王蕾)
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Traces of Besov, Triebel-Lizorkin and Sobolev Spaces on Metric Spaces
Analysis and Geometry in Metric Spaces, 2017 We establish trace theorems for function spaces defined on general Ahlfors regular metric spaces Z. The results cover the Triebel-Lizorkin spaces and the Besov spaces for smoothness indices s < 1, as well as the first order Hajłasz-Sobolev space M1,p(Z).
Saksman Eero, Soto Tomás
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Littlewood, Paley and almost‐orthogonality: a theory well ahead of its time
Journal of the London Mathematical Society, Volume 113, Issue 5, May 2026.Abstract The classic paper by Littlewood and Paley [J. Lond. Math. Soc. (1), 6 (1931), 230–233] marked the birth of Littlewood–Paley theory. We discuss this paper and its impact from a historical perspective, include an outline of the results in the paper and their subsequent significance in relation to developments over the last century, and set them ...
Anthony Carbery
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Zhejiang Daxue xuebao. Lixue ban, 2003 类似Plauszynski相应定理的证明方法,研究了Marcinkiewicz交换子Cb在Triebel-Lizorkin空间的有界性质,得到如下结果 ...
CHENDong-xiang(陈冬香) +1 more
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Generalized quasi‐geostrophic equation in critical Lorentz–Besov spaces, based on maximal regularity
Mathematische Nachrichten, Volume 299, Issue 3, Page 637-660, March 2026.Abstract We consider the quasi‐geostrophic equation with its principal part (−Δ)α${(-\mathrm{\Delta})^{\alpha}}$ for α>1/2$\alpha >1/2$ in Rn$\mathbb {R}^n$ with n≥2$n \ge 2$. We show that for every initial data θ0∈Ḃr,q1−2α+nr$\theta _0 \in \dot{B}^{1-2\alpha + \frac{n}{r}}_{r, q}$ with 1
Hideo Kozono +2 more
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Estimates for certain class of rough generalized Marcinkiewicz functions along submanifolds
Open Mathematics, 2023 We establish certain delicate Lp{L}^{p} bounds for a class of generalized Marcinkiewicz integral operators along submanifolds with rough kernels.
Ali Mohammed, Al-Qassem Hussain
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