共查询到20条相似文献,搜索用时 15 毫秒
1.
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
2.
Consider a supercritical superprocess X = {Xt, t≥0} on a locally compact separable metric space (E,m). Suppose that the spatial motion of X is a Hunt process satisfying certain conditions and that the branching mechanism is of the form ψ ( x , λ ) = - a ( x ) λ + b ( x ) λ 2 + ∫ ( 0 , + ∞ ) ( e - λ y - 1 + λ y ) n ( x , d y ) , ? x ∈ E , λ > 0 , where a ∈ B b ( E ) , b ∈ B b + ( E ) , and n is a kernel from E to (0,+∞) satisfying sup ? x ∈ E ∫ 0 + ∞ y 2 n ( x , d y ) < + ∞ . Put T t f ( x ) = P δ x ? f , X t ? . Suppose that the semigroup {Tt; t≥0}is compact. Let λ0 be the eigenvalue of the (possibly non-symmetric) generator L of {Tt}that has the largest real part among all the eigenvalues of L, which is known to be real-valued. Let ? 0 and ? ^ 0 be the eigenfunctions of L and L ^ (the dual of L) associated with λ0, respectively. Assume λ0>0. Under some conditions on the spatial motion and the ? 0 -transform of the semigroup {Tt}, we prove that for a large class of suitable functions f, lim ? t → + ∞ e - λ 0 t ? f , X t ? = W ∞ ∫ E ? ^ 0 ( y ) f ( y ) m ( d y ) , ? P μ - a . s . , for any finite initial measure μ on E with compact support, where W∞ is the martingale limit defined by W ∞ : = lim ? t → + ∞ e - λ 0 t ? ? 0 , X t ? . Moreover, the exceptional set in the above limit does not depend on the initial measure μ and the function f. 相似文献
3.
We consider a branching random walk on N with a random environment in time (denoted by ξ). Let Zn be the counting measure of particles of generation n, and let Zn(t) be its Laplace transform. We show the convergence of the free energy n-llog Zn(t), large deviation principles, and central limit theorems for the sequence of measures {Zn}, and a necessary and sufficient condition for the existence of moments of the limit of the martingale Zn(t)/E[Zn(t)ξ]. 相似文献
4.
For a square-free integer d other than 0 and 1, let K = ? ( d ) , where ? is the set of rational numbers. Then K is called a quadratic field and it has degree 2 over ? . For several quadratic fields K = ? ( d ) , the ring Rdof integers of K is not a unique-factorization domain. For d<0, there exist only a finite number of complex quadratic fields, whose ring Rd of integers, called complex quadratic ring, is a unique-factorization domain, i.e., d = −1,−2,−3,−7,−11,−19,−43,−67,−163. Let ϑ denote a prime element of Rd, and let n be an arbitrary positive integer. The unit groups of R d / 〈 v n 〉 was determined by Cross in 1983 for the case d = −1. This paper completely determined the unit groups of R d / 〈 v n 〉 for the cases d = −2,−3. 相似文献
5.
Yuchao WANG 《Frontiers of Mathematics in China》2015,10(6):1449
value of a given binary linear form at prime arguments. Let λ1 and λ2 be positive real numbers such that λ1/λ2 is irrational and algebraic. For any (C, c) well-spaced sequence V and δ>0, let E(V , X, δ) denote the number of υ∈V with υ≤X for which the inequality | λ 1 p 1 + λ 2 ρ 2 − υ | < υ − δ has no solution in primes p1, p2. It is shown that for any ε>0,we have E(V , X, δ) «max(X 3 5 + 2 δ + ε , X 2 3 + 4 3 δ + ε ). 相似文献
6.
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
7.
Complex Hermitian Clifford analysis emerged recently as a refinement of the theory of several complex variables, while at the same time, the theory of bicomplex numbers motivated by the bicomplex version of quantum mechanics is also under full development. This stimulates us to combine the Hermitian Clifford analysis with the theory of bicomplex number so as to set up the theory of bicomplex Hermitian Clifford analysis. In parallel with the Euclidean Clifford analysis, the bicomplex Hermitian Clifford analysis is centered around the bicomplex Hermitian Dirac operator | D : C ∞ ( R 4 n , W 4 n ) → C ∞ ( R 4 n , W 4 n ) , where W 4 n is the tensor product of three algebras, i.e., the hyperbolic quaternion B ^ , the bicomplex number B , and the Clifford algebra R n . The operator D is a square root of the Laplacian in R 4 n , introduced by the formula D | = ∑ j = 0 3 K j ? Z j with K j being the basis of B ^ , and ? Z j denoting the twisted Hermitian Dirac operators in the bicomplex Clifford algebra B ? R 0,4 n whose definition involves a delicate construction of the bicomplexWitt basis. The introduction of the operator D can also overturn the prevailing opinion in the Hermitian Clifford analysis in the complex or quaternionic setting that the complex or quaternionic Hermitiean monogenic functions are described by a system of equations instead of by a single equation like classical monogenic functions which are null solutions of Dirac operator. In contrast to the Hermitian Clifford analysis in quaternionic setting, the Poisson brackets of the twisted real Clifford vectors do not vanish in general in the bicomplex setting. For the operator D , we establish the Cauchy integral formula, which generalizes the Martinelli-Bochner formula in the theory of several complex variables. 相似文献
8.
Let K be the familiar class of normalized convex functions in the unit disk. Keogh and Merkes proved the well-known result that max ? f ∈ K | a 3 − λ a 2 2 | ≤ max ? { 1 / 3 , | λ − 1 | } , λ ∈ ? , and the estimate is sharp for each λ. We investigate the corresponding problem for a subclass of quasi-convex mappings of type B defined on the unit ball in a complex Banach space or on the unit polydisk in ? n . The proofs of these results use some restrictive assumptions, which in the case of one complex variable are automatically satisfied. 相似文献
9.
Xie-Bin CHEN 《Frontiers of Mathematics in China》2019,14(6):1117
We consider the problem of existence of a Hamiltonian cycle containing a matching and avoiding some edges in an n-cube , and obtain the following results. Let , and with . If M is a matching and every vertex is incident with at least two edges in the graph , then all edges of M lie on a Hamiltonian cycle in . Moreover, if or , then the upper bound of number of faulty edges tolerated is sharp. Our results generalize the well-known result for . 相似文献
10.
Similar to the property of a linear Calderdn-Zygmund operator, a linear fractional type operator Is associated with a BMO function b fails to satisfy the continuity from the Hardy space Hp into Lp for p ≤ 1. Thus, an alternative result was given by Y. Ding, S. Lu and P. Zhang, they proved that [b,Iα] is continuous from an atomic Hardy space Hp b into Lp, where Hp b is a subspace of the Hardy space Hp for n/(n + 1) 〈 p ≤ 1. In this paper, we study the commutators of multilinear fractional type operators on product of certain Hardy spaces. The endpoint (Hp1 b1 ×... × HP2, Lp) boundedness for multilinear fractional type operators is obtained. We also give the boundedness for the commutators of multilinear Calderdn-Zygmund operators and multilinear fractional type operators on product of certain Hardy spaces when b ∈ (Lipβ)m(Rn). 相似文献
11.
We introduce the generalized area operators by using nonnegative measures defined on upper half-spaces ? + n + 1 . The characterization of the boundedness and compactness of the generalized area operator from Lp(? n ) to Lq(? n ) is investigated in terms of s-Carleson measures with 1<p, q<+∞. In the case of p = q = 1, the weak type estimate is also obtained. 相似文献
12.
We investigate k-uniform loose paths. We show that the largest Heigenvalues of their adjacency tensors, Laplacian tensors, and signless Laplacian tensors are computable. For a k-uniform loose path with length l ≥ 3 , we show that the largest H-eigenvalue of its adjacency tensor is ( ( 1 + 5 ) / 2 ) 2 / k when l = 3 and λ ( A ) = 3 1 / k when l = 4 , respectively. For the case of l ≥ 5 , we tighten the existing upper bound 2. We also show that the largest H-eigenvalue of its signless Laplacian tensor lies in the interval (2, 3) when l ≥ 5 . Finally, we investigate the largest H-eigenvalue of its Laplacian tensor when k is even and we tighten the upper bound 4. 相似文献
13.
Let G be a simple connected graph, and let d i be the degree of its i-th vertex. The sum-connectivity index of the graph G is defined as χ ( G ) = Σ v i v j ∈ E ( G ) ? ( d i + d j ) − 1 / 2 . We discuss the effect on χ(G) of inserting an edge into a graph. Moreover, we obtain the relations between sum-connectivity index and Randić index. 相似文献
14.
Shangquan BU 《Frontiers of Mathematics in China》2015,10(2):239
Using known operator-valued Fourier multiplier results on vectorvalued H?lder continuous function spaces, we completely characterize the wellposedness of the degenerate differential equations ( M u ) ' ( t ) = A u ( t ) + f ( t ) for t ∈ R in H?lder continuous function spaces C a ( R ; X ) by the boundedness of the M-resolvent of A, where A and M are closed operators on a Banach space X satisfying D ( A ) ? D ( M ) . 相似文献
15.
Submanifolds in space forms satisfy the well-known DDVV inequality. A submanifold attaining equality in this inequality pointwise is called a Wintgen ideal submanifold. As conformal invariant objects, Wintgen ideal submanifolds are investigated in this paper using the framework of M?bius geometry. We classify Wintgen ideal submanfiolds of dimension m ≥ 3 and arbitrary codimension when a canonically defined 2-dimensional distribution ? 2 is integrable. Such examples come from cones, cylinders, or rotational submanifolds over super-minimal surfaces in spheres, Euclidean spaces, or hyperbolic spaces, respectively. We conjecture that if ? 2 generates a k-dimensional integrable distribution ? k and k<m, then similar reduction theorem holds true. This generalization when k = 3 has been proved in this paper. 相似文献
16.
17.
For n = 2 or 3 and , we study the oscillatory hyper Hilbert transform along an appropriate variable curve in (namely, is a curve in for each fixed x), where . We obtain some boundedness theorems of , under some suitable conditions on and . These results are extensions of some earlier theorems. However, is not a convolution in general. Thus, we only can partially employ the Plancherel theorem, and we mainly use the orthogonality principle to prove our main theorems. 相似文献
18.
Miao LOU 《Frontiers of Mathematics in China》2019,14(1):123-134
Let f be a full-level cusp form for GLm(Z) with Fourier coefficients Af(cm-2,…, c1, n): Let λ(n) be either the von Mangoldt function Λ(n) or the k-th divisor function τk(n): We consider averages of shifted convolution sums of the type Σ|h|≤H |ΣX相似文献
19.
Fei HOU 《Frontiers of Mathematics in China》2015,10(6):1325
Let L(s, sym2f) be the symmetric-square L-function associated to a primitive holomorphic cusp form f for SL(2,? ), with tf(n,1) denoting the nth coefficient of the Dirichlet series for it. It is proved that, for N≥2 and any α ∈ ? , there exists an effective positive constant c such that ∑ n ≤ N Λ ( n ) t f ( n , 1 ) e ( n α ) ≪ N exp ⁡ ( − c log ⁡ N ) , where Λ(n) is the von Mangoldt function, and the implied constant only depends on f. We also study the analogue of Vinogradov’s three primes theorem associated to the coefficients of Rankin-Selberg L-functions. 相似文献
20.
Let be a supercritical branching process in an independent and identically distributed random environment. We prove Cramér moderate deviations and Berry-Esseen bounds for log( ) uniformly in ,which extend the corresponding results by I. Grama, Q. Liu, and M. Miqueu [Stochastic Process. Appl., 2017, 127: 1255–1281] established for . The extension is interesting in theory, and is motivated by applications. A new method is developed for the proofs; some conditions of Grama et al. are relaxed in our present setting. An example of application is given in constructing confidence intervals to estimate the criticality parameter in terms of log( ) and n. 相似文献