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1.
Nandi  Debanjan  Rajala  Tapio  Schultz  Timo 《Potential Analysis》2019,51(4):483-498
Potential Analysis - We show that in a bounded simply connected planar domain Ω the smooth Sobolev functions Wk,∞(Ω) ∩ C∞(Ω) are dense in the homogeneous Sobolev...  相似文献   

2.
On a compact Riemannian manifold,we prove a decomposition theorem for arbitrarily bounded energy sequence of solutions of a singular elliptic equation.  相似文献   

3.
给出了齐型空间上Lipschitz函数空间的两个新的等价范数,证明了Lipschitz函数满足与BMO函数类似的Joho-Nirenberg型不等式.  相似文献   

4.
In this paper, two theorems about the compactness of almost invariant operators on homogeneous Banach spaces of distributions (in the sense of Feichtinger [11]) defined on a locally compact abelian group are proved. Our theorems generalize the corresponding results of K. de Leeuw [3] and Tewari and Madan [18] for operators on homogeneous Banach spaces on the circle group and Segal algebras on a compact abelian groups, respectively.AMS Subject Classification 2000: 43A85, 47B07.  相似文献   

5.
He  Ziyi  Han  Yongsheng  Li  Ji  Liu  Liguang  Yang  Dachun  Yuan  Wen 《Journal of Fourier Analysis and Applications》2019,25(5):2197-2267
Journal of Fourier Analysis and Applications - Let $$(X,d,\mu )$$ be a space of homogeneous type, with the upper dimension $$\omega $$ , in the sense of Coifman and Weiss. Assume that $$\eta $$ is...  相似文献   

6.
设X是齐型空间.设T_(j,1)和T_(j,2)是具有非光滑核的奇异积分算子,或者是±II(I是恒等算子).令Toeplitz型算子T_b=■T_(j,1)M_T_(j,2),其中M_bf(x)=b(x)f(x).研究了当b∈BMO(X)时,T_b(f)在加权情况下的有界性,以及当b∈BMO(X)时,与经典Carderon-Zygmund算子相联的T_b(f)在Morrey空间上的有界性.  相似文献   

7.
设X是齐型空间.设Tj,1和Tj,2是具有非光滑核的奇异积分箅子,或者是±I(I是恒等算子).令Toeplitz型算子Tb=N∑j=1Tj,1MbTj,2,其中Mbf(x)=6(x)f(x).研究了当b∈BMO(X)时,Tb(f)在加权情况下的有界性,以及当b∈BMO(X)时,与经典Carderón-Zygmund算子相联的Tb(f)在Morrey空间上的有界性.  相似文献   

8.
Abstract

We consider a scalar field equation on compact surfaces which has variational structure. When the surface is a torus and a physical parameter ρ belongs to (8π,4π2) we show under some extra assumptions that, besides a local minimum, the functional admits at least other two saddle points.  相似文献   

9.
This paper is concerned with a compact difference scheme with the truncation error of order 3/2 for time and order 4 for space to an evolution equation with a weakly singular kernel. The integral term is treated by means of the second order convolution quadrature suggested by Lubich. The stability and convergence are proved by the energy method. A numerical experiment is reported to verify the theoretical predictions.  相似文献   

10.
In [5] the embedding theorem for the Besov spaces Bdot\A,qpBdot^{\A,q}_p with $\minus \varepsilon < \alpha \varepsilon $\minus \varepsilon < \alpha \varepsilon and 1 £ p1 \le p, q £ ¥q \le \infty, and Triebel-Lizorkin spaces \Fdot\A,qp\Fdot^{\A,q}_p with $\minus \varepsilon < \alpha \varepsilon $\minus \varepsilon < \alpha \varepsilon and 1 £ p1 \le p, q £ ¥q \le \infty, on spaces of homogeneous type was obtained. In this article the embedding theorem is generalized to the Besov spaces Bdot\A,qpBdot^{\A,q}_p with $p_0 < p \le \infty $p_0 < p \le \infty and 0 < q \le \infty for for p_0 < 1, and the Triebel-Lizorkin spaces, and the Triebel-Lizorkin spaces \Fdot^{\A,q}_pwith with p_1 < p < \inftyand and p_1 < q < \infty for for p_1< 1. The proofs are new even for. The proofs are new even for \mathbb{R}^n$.  相似文献   

11.
12.
胡国恩  王卫红 《数学学报》2010,53(1):141-152
本文建立齐型空间上与奇异积分算子和BMO构成的交换子相应的极大算子的一个带一般权的加权L~p估计.  相似文献   

13.
We prove the formality property of any homogeneous space G/G generated by an automorphism of finite order of a compact simple Lie group G.  相似文献   

14.
We address the local existence of solutions of the 2D and 3D water wave problems. For the space dimension three, we consider the irrotational datum u 0 and prove that the local in time existence holds for initial velocities belonging to H 2.5+δ , where δ>0 is arbitrary. For the space dimension two, the data does not need to be irrotational. We prove the local in time existence when u 0 belongs to H 2+δ and $\operatorname{curl}u_{0}$ to H 1.5+δ , where δ>0 is arbitrary.  相似文献   

15.
This paper introduces a unified operator theory approach to the abstract Fourier analysis over homogeneous spaces of compact groups. Let G be a compact group and H be a closed subgroup of G. Let G/H be the left coset space of H in G andμ be the normalized G-invariant measure on G/ H associated to the Weil's formula.Then, we present a generalized abstract framework of Fourier analysis for the Hilbert function space L~2(G/H,μ).  相似文献   

16.
The Schwarz reflection principle in one complex variable can be stated as follows. Let M and M′ be two real analytic curves in ? and f a holomorphic function defined on one side of M, extending continuously through M, and mapping M into M′. Then f has a holomorphic extension across M. In this paper, we extend this classical theorem to higher complex dimensions for a class of hypersurfaces of infinite type.  相似文献   

17.
Compact manifolds embedded in Euclidean space which have a transitive group G of linear isometries, such as the spheres with the rotation group or the “flat” tori with the group of rotations in each coordinate direction, admit a natural notion of a continuous G-invariant kernel function k(xy), which generalizes the idea of a radial or distance-dependent function on the spheres and tori. In connection with a study of quasi-interpolation on these spaces, we have reproved and extended results of Sun for the spheres to characterize those kernels for which the span of the translates, ∑ ank(xyn), is dense in the continuous functions. The essence of the characterization is that the integral operator with G-invariant kernel k(xy) must be non-singular when restricted to the space of nth degree polynomial functions. This requires that the polynomials be invariant under all such linear operators, which is true for many compact homogeneous M including the spheres, tori, and others. In fact the non-singularity must hold only on any finite-dimensional space of zonal polynomials, those which are pointwise fixed by the subgroup of all isometries fixing a single point on M. In practical terms this later condition is verified by choosing one point on the manifold (the north pole on the spheres or the identity element on the flat tori), picking some basis for the polynomials of given degree which are fixed under the isometries leaving the pole invariant, and testing whether the integral operator (which leaves this space invariant) has a non-singular matrix. In all the cases considered, where the family of G-invariant kernels lead to commuting operator families, there are diagonalizing bases for this restricted operator, and the characterization becomes the non-vanishing of the appropriate Fourier-like coefficients.  相似文献   

18.
§ 1.Introduction Letabeameasurablefunction ,bea φ∈S(R)nonnegativefunction ,and 0 <r <∞ .Definecommutatorsasfollows :Cra( f) (x) =supx∈Q1|Q|∫Q|a(x) -a( y) |r|f( y) |dy ,( 1 .1 )andΦra( f) (x) =supε>0∫Rn|a(x) -a( y) |rφε( |x- y|)|f( y) |dy ,( 1 .2 )whereQdenotesacubeandφε(t) =1εnφ tε .Thesetwooperat…  相似文献   

19.
邱道文 《数学进展》2003,32(3):345-355
设(x,d,μ)是齐型空间.本文证明了分数次积分算子Iα与VMO函数构成的交换子I^ba是L^p(X)到L^q(X)的紧算子,其中α∈(0,1),1<p<q<∞且1/q=1/p—α。  相似文献   

20.
齐型空间上的Herz空间及其应用   总被引:7,自引:0,他引:7  
定义了一类齐型空间上的Herz空间及弱Herz空间,研究了定义在这些空间中的一类次线性算子的性质.  相似文献   

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