Results 61 to 70 of about 5,281,258 (136)

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, Shiwei Cao, Qinghua Zhang, Dengfeng Lu   +3 more
wiley   +1 more source

Classifying Triebel–Lizorkin Capacities in Metric Spaces [PDF]

Journal of Fourier Analysis and Applications
We study nonlocal or fractional capacities in metric measure spaces. Our main goal is to clarify the relations between relative Hajłasz–Triebel–Lizorkin capacities, potentional Triebel–Lizorkin capacities, and metric space variants of Riesz capacities ...
Juha Lehrback, Kaushik Mohanta, Antti V. Vahakangas   +2 more
semanticscholar   +1 more source

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
wiley   +1 more source

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
doaj   +1 more source

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
wiley   +1 more source

Sharp function estimates and boundedness for Toeplitz-type operators associated with general fractional integral operators

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
doaj   +1 more source

Asymptotic estimates of solution to damped fractional wave equation

Journal of Inequalities and Applications
It 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
doaj   +1 more source

The molecular characterizations of variable Triebel-Lizorkin spaces associated with the Hermite operator and its applications [PDF]

Journal of Approximation Theory
In this article, we introduce inhomogeneous variable Triebel-Lizorkin spaces, $F_{p(\cdot),q(\cdot)}^{\alpha(\cdot),H}(\mathbb R^n)$, associated with the Hermite operator $H:=-\Delta+|x|^2$, where $\Delta$ is the Laplace operator on $\mathbb R^n$, and ...
Qi Sun, Ci-Qiang Zhuo
semanticscholar   +1 more source

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
doaj   +1 more source

Continuity of multilinear operators on Triebel-Lizorkin spaces

Journal of Inequalities and Applications, 2006
The continuity of some multilinear operators related to certain convolution operators on the Triebel-Lizorkin space is obtained. The operators include Littlewood-Paley operator and Marcinkiewicz operator.
Liu Lanzhe
doaj