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The besov space B_1^(0.1) on Domains

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Acta Mathematica Sinica,English Series 2001年第2期17卷 181-196页

作者： Yi Qing GUI Shan Zhen LU Da Chun YANG Department of Mathematics. Beijing Normal University. Beijing 100875. P. R. China Department of Mathematics Beijing Normal University Beijing 100875 P. R. China

Let Ω be a bounded Lipschitz domain. Define B1,r0.1（Ω）={f∈L1（Ω）: there is an F∈ B10.1（Rn） such that F|Ω=f| and B1,z0.1（Ω）={f∈B10.1（Rn）: f=0 on Rn\}. In this paper, the authors establish the atomic decompositions of these spaces. As by-products, the authors obtained the regularity on these spaces of the solutions to the Dirichlet problem and the Neumann problem of the Laplace equation on R+n.

关键词： besov space Lipschitz domain Atom Laplace equation

Local Well-Posedness for the Hyperelastic Rots Equation in besov space

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Journal of Mathematical Research with Applications 2016年第2期36卷 213-222页

作者： Shenggui LIU Department of Mathematics Jiaying University

This paper is concerned with the cauchy problem for the hyperelastic rots equation in besov space. By virtue of the Littlewood-Paley decomposition, the local well-posedness for the equation in besov space is establish... 详细信息

关键词： Hyperelastic rots equations Cauchy problem local well-posedness blow-up criterion besov space

Global existence for the two-dimensional Euler equations in a critical besov space

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Global existence for the two-dimensional Euler equations in ...

Regularity Criterion of Weak Solutions to the 3D Micropolar Fluid Equations in besov space

The 2011 International Conference on Advanced Materials and Information Technology Processing(AMITP 2011)

作者： Kun Qu Yue Zhang School of Science Dalian Jiaotong University

In this paper we prove the global existence for the two-dimensional Euler equations in the critical besov space B3 1,1(R2). Making use of a new estimate of transport equation and Littlewood-Paley theory, we get the gl... 详细信息

关键词： Euler equations Global existence besov space

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Chinese Quarterly Journal of Mathematics 2020年第4期35卷 418-423页

作者： LI Xiao Department of Mathematics Teaching and Research Huanghe Jiaotong UniversityHenan454000China

This paper studies the regularity criterion of weak solutions to the micropolarfluid equations in three dimensions. Let (■u∈L2/2-γ(0,T;B^-γ∞,∞),■ω∈L^2(0,T;B^-1∞,∞)),it is showed that the weak solution(u,ω)... 详细信息

关键词： Micropolar fluid equations Regularity criteria besov space

besov spaceS AND K-FUNCTIONALS IN L_p, 0

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Acta Mathematicae Applicatae Sinica 2000年第3期16卷 258-265页

作者：李松吴正昌马柏林 Department of Mathematics Zhejiang University Hangzhou China Department of Applied Mathematics Huna University Changsha China

We investigate besov spaces and their connection with trigonometric polynomial approximation in L_p[－π,π], algebraic polynomial approximation in L_p[-1,1], algebraic polynomial approximation in L_p(S), and entire function of exponential type approximation in Lp(R), and characterize K-functionals for certain pairs of function spaces including (Lp [-π,π], B_s~α (Lp[-π，π])), (L_p(R),B_s~α (Lp(R))), (Lp[-1,1],B_s~α (Lp[-1,1])), and (Lp(S),B_s~α (Lp(S))), where 0

关键词： besov space K-functional Lp space (0

The Commutators of Fractional Integrals on besov spaces

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Acta Mathematica Sinica,English Series 2004年第3期20卷 405-414页

作者： WenGuCHEN ShanZhenLU InstituteofAppliedPhysicsandComputationalMathematics P.O.Box8009Beijing100088P.R.China DepartmentofMathematics BeijingNormalUniversityBeijing100875P.R.China

In this paper we consider the commutators of fractional integrals

关键词： Commutator Paraproduct besov space

Jacobian-determinant Equation in the Critical besov spaces

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Acta Mathematica Sinica,English Series 2017年第5期33卷 691-704页

作者： Xiang Rong ZHU Department of Mathematics Zhejiang Normal University Jinhua 321004 P. R. China

Let Ω be a bounded domain in R;with smooth boundary. Here we consider the following Jacobian-determinant equation det u（x）=f（x）,x∈Ω;u（x）=x,x∈?Ω where f is a function on Ω with min;f = δ > 0 and Ωf（x）dx = |Ω|. We prove that if f ∈B;（Ω） for some p∈（n,∞）, then there exists a solution u ∈ B;（Ω）C;（Ω） to this equation. On the other hand, we give a simple example such that u ∈ C;（R;, R;） while detu does not lie in B;（R;） for any p<∞.

关键词： Jacobian-determinant besov space elliptic system Neumann problem

Variable integral and smooth exponent besov spaces associated to non-negative self-adjoint operators

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Frontiers of Mathematics in China 2020年第6期15卷 1245-1263页

作者： Jingshi XU School of Mathematics and Computing Science Guilin University of Electronic TechnologyGuilin 541004China

We introduce the variable integral and the smooth exponent besov spaces associated to non-negative self-adjoint *** we give the equivalent norms via the Peetre type maximal functions and atomic decomposition of these ... 详细信息

关键词： besov space variable exponent maximal function non negative self-adjoint operators atomic decomposition

GENERALIZED besov spaceS AND TRIEBEL-LIZORKIN spaceS

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Analysis in Theory and Applications 2008年第4期24卷 336-350页

作者： Huikun Jiang Chin-Cheng Lin Nanjing University China National Central University China（Taiwan）

In this paper the classical besov spaces B^sp.q and Triebel-Lizorkin spaces F^sp.q for s∈R are generalized in an isotropy way with the smoothness weights { ｜2j｜^α→ln }7=0. These generalized besov spaces and Triebel-Lizorkin spaces, denoted by B^α→p.q and F^α→p.q for α^→ E Nk and k ∈N, respectively, keep many interesting properties, such as embedding theorems （with scales property for all smoothness weights）, lifting properties for all parameters 5, and duality for index 0 〈 p 〈∞ By constructing an example, it is shown that there are infinitely many generalized besov spaces and generalized Triebel-Lizorkin spaces lying between B^sp.q and ∪t〉s B^tp.q, and between F^sp.q and ∪t〉s F^tp.q, respectively.

关键词： besov space embedding theorem function space of generalized smoothness,Triebell-Lizorkin space