共查询到20条相似文献,搜索用时 15 毫秒
1.
Let (X, d, μ) be a metric measure space with non-negative Ricci curvature. This paper is concerned with the boundary behavior of harmonic function on the (open) upper half-space . We derive that a function f of bounded mean oscillation (BMO) is the trace of harmonic function on , whenever u satisfies the following Carleson measure condition where denotes the total gradient and denotes the (open) ball centered at with radius . Conversely, the above condition characterizes all the harmonic functions whose traces are in BMO space. 相似文献
2.
Let be a complete Riemannian manifold with , and let be two complete totally geodesic submanifolds in M. We prove that if n1 + n2 = n − 2 and if the distance , then Mi is isometric to , or with the canonical metric when ni>0, and thus, M is isometric to , or except possibly when n = 3 and M1 (or M2) with or n = 4 and M1 (or M2) . 相似文献
3.
Let X be a ball quasi-Banach function space satisfying some mild additional assumptions and the associated Hardy-type space. In this article, we first establish the finite atomic characterization of . As an application, we prove that the dual space of is the Campanato space associated with X. For any given and , using the atomic and the Littlewood–Paley function characterizations of ,we also establish its s-order intrinsic square function characterizations, respectively, in terms of the intrinsic Lusin-area function ,the intrinsic g-function ,and the intrinsic -function , where λ coincides with the best known range. 相似文献
4.
At each time be a random sequence of non-negative numbers that are ultimately zero in a random environment . The existence and uniqueness of the nonnegative fixed points of the associated smoothing transformation in random environment are considered. These fixed points are solutions to the distributional equation for ,where are random variables in random environment which satisfy that for any environment ; under ; are independent of each other and , and have the same conditional distribution where T is the shift operator. This extends the classical results of J. D. Biggins [J. Appl. Probab., 1977, 14: 25-37] to the random environment case. As an application, the martingale convergence of the branching random walk in random environment is given as well. 相似文献
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6.
We consider a pendulum type equation with p-Laplacian , where and p(t) are 1-periodic about every variable. The solutions of this equation present two interesting behaviors. On the one hand, by applying Moser's twist theorem, we find infinitely many invariant tori whenever which yields the bounded-ness of all solutions and the existence of quasi-periodic solutions starting at t = 0 on the invariant tori. On the other hand, if p(t) = 0 and has some specific forms, we find a full symbolic dynamical system made by solutions which oscillate between any two different trivial solutions of the equation. Such chaotic solutions stay close to the trivial solutions in some fixed intervals, according to any prescribed coin-tossing sequence. 相似文献
7.
Let φ be a growth function, and let A : = - ( ? - i a ) ? ( ? - i a ) + V be a magnetic Schr?dinger operator on L 2 ( ? n ) , n ≥ 2 , where α : = ( α 1 , α 2 , ? , α n ) ∈ L l o c 2 ( ? n , ? n ) and 0 ≤ V ∈ L l o c 1 ( ? n ) . We establish the equivalent characterizations of the Musielak-Orlicz-Hardy space H A , φ ( ? n ) , defined by the Lusin area function associated with { e - t 2 A } t > 0 , in terms of the Lusin area function associated with { e - t A } t > 0 , the radial maximal functions and the nontangential maximal functions associated with { e - t 2 A } t > 0 and { e - t A } t > 0 , respectively. The boundedness of the Riesz transforms L k A - 1 / 2 , k ∈ { 1 , 2 , ? , n } , from H A , φ ( ? n ) to L φ ( ? n ) is also presented, where Lk is the closure of ? ? x k - i α k in L 2 ( ? n ) . These results are new even when φ ( x , t ) : = ω ( x ) t p for all x ∈ ? n and t ∈(0,+∞) with p ∈(0, 1] and ω ∈ A ∞ ( ? n ) (the class of Muckenhoupt weights on ? n ). 相似文献
8.
Existence and multiplicity results for nonlinear Schrödinger-Poisson equation with general potential
Yuan SHAN 《Frontiers of Mathematics in China》2020,15(6):1189
This paper is concerned with the Schrödinger-Poisson equation Under certain hypotheses on V and a general spectral assumption, the existence and multiplicity of solutions are obtained via variational methods. 相似文献
9.
The regularity of random attractors is considered for the non-autonomous fractional stochastic FitzHugh-Nagumo system.We prove that the system has a pullback random attractor that is compact in Hs(Rn)×L2(Rn)and attracts all tempered random sets of L2(Rn)×L2(Rn)in the topology of Hs(Rn)×L2(Rn)with s∈(0,1).By the idea of positive and negative truncations,spectral decomposition in bounded domains,and tail estimates,we achieved the desired results. 相似文献
10.
Let X^ε be a small perturbation Wishart process with values in the set of positive definite matrices of size m, i.e., the process X^ε is the solution of stochastic differential equation with non-Lipschitz diffusion coefficient: dXt^ε = √εXt^εtdBt' + dBt'√εXt^ε + ρImdt, X0 = x, where B is an rn x m matrix valued Brownian motion and B' denotes the transpose of the matrix B. In this paper, we prove that { (Xt^ε-Xt^0)/√εh^2(ε),ε 〉 0} satisfies a large deviation principle, and (Xt^ε - Xt^0)/√ε converges to a Gaussian process, where h(ε) → +∞ and √ε h(ε) →0 as ε →0. A moderate deviation principle and a functional central limit theorem for the eigenvalue process of X^ε are also obtained by the delta method. 相似文献
11.
This paper deals with anisotropic solutions u ∈ W 1 , ( p i ) ( Ω , ? N ) to the nonlinear elliptic system − Σ i = 1 n D i ( a i α ( χ , D u ( χ ) ) ) = − Σ i = 1 n D i F i α ( χ ) , α = 1 , 2 , ... , N , We present a monotonicity inequality for the matrix a = ( a i α ) ∈ ? N × n , whichguarantees global pointwise bounds for anisotropic solutionsu . 相似文献
12.
Consider the generalized dispersive equation defined by{iδtu+Ф(√-△)u=0,(x,t)∈R^n×R,u(x,0)=f(x),F∈F(R^n),(*)whereФ(√-△)is a pseudo-differential operator with symbolФ(|ζ|).In the present paper,assuming thatФsatisfies suitable growth conditions and the initial data in H^s(R^n),we bound the Hausdorff dimension of the sets on which the pointwise convergence of solutions to the dispersive equations(*)fails.These upper bounds of Hausdorff dimension shall be obtained via the Kolmogorov-Seliverstov-Plessner method. 相似文献
13.
We first consider the group inverses of the block matrices ( A 0 B C ) over a weakly finite ring. Then we study the sufficient and necessary conditions for the existence and the representations of the group inverses of the block matrices ( A C B D ) over a ring with unity 1 under the following conditions respectively: (i) B = C, D = 0, B# and (BπA) # both exist; (ii) B is invertible and m = n; (iii) A# and (D - CA#B)# both exist, C = CAA# , where A and D are m × m and n × n matrices, respectively. 相似文献
14.
Assuming that the operators L1, L2 are self-adjoint and satisfy the generalized Davies-Gaffney estimates, we shall prove that the weighted Hardy space associated to operators L1, L2 on product domain, which is defined in terms of area function, has an atomic decomposition for some weight . 相似文献
15.
Meng ZHANG 《Frontiers of Mathematics in China》2016,11(2):449-460
We prove that almost all positive even integers n can be written as n = p 2 2 + p 3 3 + p 4 4 + p 5 5 with | p k k - N 4 | ≤ N 321 325 + ? for 2≤k≤5. Moreover, it is proved that each sufficiently large odd integer N can be represented as N = p 1 + p 2 2 + p 3 3 + p 4 4 + p 5 5 with | p k k - N 5 | ≤ N 321 325 + ? for 1≤k≤5. 相似文献
16.
A finite group G is said to be a Bn-group if any n-element subset A = {a1, a2,..., an} of G satisfies . In this paper, the characterizations of the B6- and B7-groups are given. 相似文献
17.
Let(Ai,φi,i+1) be a generalized indue Live system of a sequeiiee (Ai) of unital separable C^*-algebras,with A =limi→∞(Ai,φi,i+1). Set φj,i=φi-1,i^0…0φj+1,j+2^0 φj,j+1 for all i>j. We prove that if φj,i are order zero completely positive contractions for all j and i>j, And L:=inf{λ|λ∈σ(φj,i(1Aj)) for all j uud i>j}>0, where σ(φj,i(1Aj)) is the speetrum of φj,i(1Aj),than limi→∞(Cu(Ai),Cu((φi,i+1))=Cu(A), where Cu(A) is a stable version of the Cuntz semigroup of C^*-algebra A. Let (An,φm,n) be a generalized inductive syfitem of C^*-algahrafl, with the ipmkn order zero completely positive contractions. We also prove that if the decomposition rank (nuclear dimension) of ,4n is no more t han some integer k for each n, then the decompostition rank (nuclear dimension) of A is also no more than k. 相似文献
18.
Let λ1, λ2, λ3, λ4 be non-zero real numbers, not all of the same sign, w real. Suppose that the ratios λ1/λ2, λ1/λ3 are irrational and algebraic. Then there are in.nitely many solutions in primes pj, j =1, 2, 3, 4, to the inequality . This improves the earlier result. 相似文献
19.
Let (Xt)t≥0 be a symmetric strong Markov process generated by non-local regular Dirichlet form (D, D (D)) as follows: D ( f , g ) = ∫ ? d ∫ ? d ( f ( x ) - f ( y ) ) ( g ( x ) - g ( y ) ) J ( x , y ) d x d y , ? f , g ∈ D ( D ) , where J(x, y) is a strictly positive and symmetric measurable function on ? d × ? d . We study the intrinsic hypercontractivity, intrinsic supercontractivity, and intrinsic ultracontractivity for the Feynman-Kac semigroup T t V ( f ) ( x ) = E x ( exp ? ( - ∫ 0 t V ( X s ) d s ) f ( X t ) ) , ? x ∈ ? d , f ∈ L 2 ( ? d ; d x ) . In particular, we prove that for J ( x , y ) ≈ | x - y | - d - a l { | x - y | ≤ 1 } + e - | x - y | l { | x - y | > 1 } with α ∈(0, 2) and V ( x ) = | x | λ with λ>0, ( T t V ) t ≥ 0 is intrinsically ultracontractive if and only if λ>1; and that for symmetric α-stable process (Xt)t≥0 with α ∈(0, 2) and V ( x ) = log ? λ ( 1 + | x | ) with some λ>0, ( T t V ) t ≥ 0 is intrinsically ultracontractive (or intrinsically supercontractive) if and only if λ>1, and ( T t V ) t ≥ 0 is intrinsically hypercontractive if and only if λ ≥ 1 . Besides, we also investigate intrinsic contractivity properties of ( T t V ) t ≥ 0 for the case that lim inf ? | x | → + ∞ V ( x ) < + ∞ 相似文献
20.
Suppose that the vertex set of a graph G is . The transmission (or Di) of vertex vi is defined to be the sum of distances from vi to all other vertices. Let be the diagonal matrix with its (i, i)-entry equal to . The distance signless Laplacian spectral radius of a connected graph G is the spectral radius of the distance signless Laplacian matrix of G, defined as , where is the distance matrix of G. In this paper, we give a lower bound on the distance signless Laplacian spectral radius of graphs and characterize graphs for which these bounds are best possible. We obtain a lower bound on the second largest distance signless Laplacian eigenvalue of graphs. Moreover, we present lower bounds on the spread of distance signless Laplacian matrix of graphs and trees, and characterize extremal graphs. 相似文献