Results 41 to 50 of about 97 (96)
Global Solvability of the Generalized Navier−Stokes System in Critical Besov Spaces
Journal of Mathematics, Volume 2026, Issue 1, 2026.This paper is devoted to the global solvability of the Navier−Stokes system with a fractional Laplacian (−Δ)α in Rn for n ≥ 2, where the convective term has the form (|u|m−1u)·∇u for m ≥ 1. By establishing the estimates for the difference u1m−1u1−u2m−1u2 in homogeneous Besov spaces and employing the maximal regularity property of (−Δ)α in Lorentz−Besov
Huiyang Zhang +3 more
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Persistence of the solution to the Euler equations in an end‐point critical Triebel–Lizorkin space
Mathematical Methods in the Applied Sciences, Volume 48, Issue 2, Page 2421-2433, 30 January 2025.Local stay of the solutions to the Euler equations for an ideal incompressible fluid in the end‐point Triebel–Lizorkin space F1,∞sℝd$$ {F}_{1,\infty}^s\left({\mathbb{R}}^d\right) $$ with s≥d+1$$ s\ge d+1 $$ is clarified.
JunSeok Hwang, Hee Chul Pak
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Bulletin of Mathematical SciencesLet [Formula: see text], [Formula: see text], and [Formula: see text] denote the Triebel–Lizorkin–Bourgain–Morrey space, whose special case was originally introduced by Bourgain.
Yangningrui Wan, Dachun Yang, Yirui Zhao
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New estimates of Rychkov's universal extension operator for Lipschitz domains and some applications
Mathematische Nachrichten, Volume 297, Issue 4, Page 1407-1443, April 2024.Abstract Given a bounded Lipschitz domain Ω⊂Rn$\Omega \subset \mathbb {R}^n$, Rychkov showed that there is a linear extension operator E$\mathcal {E}$ for Ω$\Omega$, which is bounded in Besov and Triebel‐Lizorkin spaces. In this paper, we introduce some new estimates for the extension operator E$\mathcal {E}$ and give some applications.
Ziming Shi, Liding Yao
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Some Function Spaces via Orthonormal Bases on Spaces of Homogeneous Type
Abstract and Applied Analysis, 2014 Let (X,d,μ) be a space of homogeneous type in the sense of Coifman and Weiss, where the quasi-metric d may have no regularity and the measure μ satisfies only the doubling property.
Chuang Chen, Ji Li, Fanghui Liao
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On Seeley‐type universal extension operators for the upper half space
Mathematische Nachrichten, Volume 297, Issue 3, Page 811-832, March 2024.Abstract Modified from the standard half‐space extension via the reflection principle, we construct a linear extension operator for the upper half space R+n$\mathbb {R}^n_+$ that has the form Ef(x)=∑j=−∞∞ajf(x′,−bjxn)$Ef(x)=\sum _{j=-\infty }^\infty a_jf(x^{\prime },-b_jx_n)$ for xn<0$x_n<0$. We prove that E$E$ is bounded in all Ck$C^k$‐spaces, Sobolev
Haowen Lu, Liding Yao
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Open Mathematics, 2021 In this paper, we establish some sharp maximal function estimates for certain Toeplitz-type operators associated with some fractional integral operators with general kernel.
Chen Dazhao, Huang Hui
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Asymptotic estimates of solution to damped fractional wave equation
Journal of Inequalities and ApplicationsIt is known that the damped fractional wave equation has the diffusive structure as t → ∞ $t\rightarrow \infty $ . Let u ( t , x ) = e − t cosh ( t L ) f ( x ) + e − t sinh ( t L ) L ( f ( x ) + g ( x ) ) $u(t,x)=e^{-t}\cosh (t\sqrt{L})f(x)+e^{-t} \frac{\
Meizhong Wang, Dashan Fan
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WEIGHTED BESOV AND TRIEBEL–LIZORKIN SPACES ASSOCIATED WITH OPERATORS AND APPLICATIONS
Forum of Mathematics, Sigma, 2020 Let $X$ be a space of homogeneous type and $L$ be a nonnegative self-adjoint operator on $L^{2}(X)$ satisfying Gaussian upper bounds on its heat kernels.
HUY-QUI BUI +2 more
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Boundedness of higher-order Marcinkiewicz-Type integrals
International Journal of Mathematics and Mathematical Sciences, 2006 Let A be a function with derivatives of order m and DγA∈Λ˙β ...
Shanzhen Lu, Huixia Mo
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