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1.
Let L=-Δ+V be a Schrödinger operator on ℝd, d≥3, where V is a non-negative compactly supported potential that belongs to Lp for some p>d/2. Let {Kt}t>0 denote the semigroup of linear operators generated by -L. For a function f we define its H1L-norm by
0} |K_t f(x)|\|_{L^1(dx)}$" align="middle" border="0">
. It is proved that for a properly defined weight w a function f belongs to H1L if and only if wf∈H1(ℝd), where H1(ℝd) is the classical real Hardy space. Mathematics Subject Classification (2000) 42B30, 35J10, 42B25 相似文献
2.
Let X be a (closed) subspace of Lp with 1≤p<∞, and let A be any sectorial operator on X. We consider associated square functions on X, of the form and we show that if A admits a bounded H∞ functional calculus on X, then these square functions are equivalent to the original norm of X. Then we deduce a similar result when X=H1(ℝN) is the usual Hardy space, for an appropriate choice of || ||F. For example if N=1, the right choice is the sum for h ∈ H1(ℝ), where H denotes the Hilbert transform. 相似文献
3.
In this paper, we study the high-dimensional fractional Hausdorff operators and establish their boundedness on the real Hardy spaces H p (? n ) for 0 < p < 1. 相似文献
4.
In this paper, we prove the product Hp boundedness of Calderón- Zygmund operators which were considered by Fefferman and Stein. The methods used in this paper are new even for the classical Hp boundedness of Calderón- Zygmund operators, namely, using some subtle estimates together with the Hp–Lp boundedness of product vector valued Calderón-Zygmund operators.This project was supported by the NNSF (No. 10271015 & No. 10310201047) of China and the second (corresponding) author was also supported by the RFDP (No. 20020027004) of China.Mathematics Subject Classification (2000):42B20, 42B30, 42B25 相似文献
5.
Let L k = (?Δ) k + V k be a Schrödinger type operator, where k ≥ 1 is a positive integer and V is a nonnegative polynomial. We obtain the L p estimates for the operators ?2k L k ?1 and ? k L k ?1/2 . 相似文献
6.
Topological free involutions on S
1 × S
n
are classified up to conjugation. We prove that this is the same as classifying quotient manifolds up to homeomorphism. There
are exactly four possible homotopy types of such quotients, and surgery theory is used to classify all manifolds within each
homotopy type. 相似文献
7.
There is a natural duality between orbits of a real form G of a complex semisimple group G
on a homogeneous rational manifold Z=G
/P and those of the complexification K
of any of its maximal compact subgroups K: (,) is a dual pair if is a K-orbit. The cycle space C() is defined to be the connected component containing the identity of the interior of {g:g() is non-empty and compact}. Using methods which were recently developed for the case of open G-orbits, geometric properties of cycles are proved, and it is shown that C() is contained in a domain defined by incidence geometry. In the non-Hermitian case this is a key ingredient for proving that C() is a certain explicitly computable universal domain.Research of the first author partially supported by Schwerpunkt Global methods in complex geometry and SFB-237 of the Deutsche Forschungsgemeinschaft.The second author was supported by a stipend of the Deutsche Akademische Austauschdienst. 相似文献
8.
Orders of the best approximations for functions of Markov-Stieltjes type in the space H p are considered in the case of intersection of the measure support and the boundary of a unit circle. The results of J.-E. Andersson for functions with a singularity at a single point of a unit circumference are extended to the case of two singularities on that circumference. 相似文献
9.
In this paper theI andII regularn-simplices are introduced. We prove that the sufficient and necessary conditions for existence of anI regularn-simplex in ℝ
n
are that ifn is even thenn = 4m(m + 1), and ifn is odd thenn = 4m + 1 with thatn + 1 can be expressed as a sum of two integral squares orn = 4m - 1, and that the sufficient and necessary condition for existence of aII regularn-simplex in ℝ
n
isn = 2m
2 - 1 orn = 4m(m + 1)(m ∈ ℕ). The connection between regularn-simplex in ℝ
n
and combinational design is given. 相似文献
10.
A. A. Yukhimenko 《Moscow University Mathematics Bulletin》2010,65(2):69-71
The system of exponents $
\left\{ {e^{i\lambda _n t} } \right\}_{n \in \mathbb{Z}}
$
\left\{ {e^{i\lambda _n t} } \right\}_{n \in \mathbb{Z}}
is considered. A sufficient condition for a Riesz-property basis in the weighted space L
p
(−π, π) is obtained. 相似文献
11.
Diarmuid Crowley 《Geometriae Dedicata》2010,148(1):15-33
We calculate \({\mathcal{S}^{{\it Diff}}(S^p \times S^q)}\), the smooth structure set of S p × S q , for p, q ≥ 2 and p + q ≥ 5. As a consequence we show that in general \({\mathcal{S}^{Diff}(S^{4j-1}\times S^{4k})}\) cannot admit a group structure such that the smooth surgery exact sequence is a long exact sequence of groups. We also show that the image of the forgetful map \({\mathcal{S}^{Diff}(S^{4j}\times S^{4k}) \rightarrow \mathcal{S}^{Top}(S^{4j}\times S^{4k})}\) is not in general a subgroup of the topological structure set. 相似文献
12.
Guy David 《Journal of Geometric Analysis》2010,20(4):837-954
We give a new proof and a partial generalization of Jean Taylor’s result (Ann. Math. (2) 103(3), 489–539, 1976) that says that Almgren almost-minimal sets of dimension 2 in ℝ3 are locally C
1+α
-equivalent to minimal cones. The proof is rather elementary, but uses a local separation result proved in Ann. Fac. Sci.
Toulouse 18(1), 65–246, 2009 and an extension of Reifenberg’s parameterization theorem (David et al. in Geom. Funct. Anal. 18, 1168–1235, 2008). The key idea is still that if X is the cone over an arc of small Lipschitz graph in the unit sphere, but X is not contained in a disk, we can use the graph of a harmonic function to deform X and substantially diminish its area. The local separation result is used to reduce to unions of cones over arcs of Lipschitz
graphs. A good part of the proof extends to minimal sets of dimension 2 in ℝ
n
, but in this setting our final regularity result on E may depend on the list of minimal cones obtained as blow-up limits of E at a point. 相似文献
13.
Bitao Cheng 《Mediterranean Journal of Mathematics》2016,13(3):1099-1116
In this paper, we consider the following nonhomogenous Schrödinger–Kirchhoff type problemwhere constants a > 0, b ≥ 0, N = 1, 2 or 3, \({V\in C(R^{N},R)}\), \({f\in C(R^{N} \times R, R)}\) and \({g\in L^{2}(R^{N})}\). Under more relaxed assumptions on the nonlinear term f that are much weaker than those in Chen and Li (Nonlinear Anal RWA 14:1477–1486, 2013), using some new proof techniques especially the verification of the boundedness of Palais–Smale sequence, a new result on multiplicity of nontrivial solutions for the problem (1.1) is obtained, which sharply improves the known result of Theorem 1.1 in Chen and Li (Nonlinear Anal RWA 14:1477–1486, 2013).
相似文献
$$\left\{ \begin{array}{ll} - (a+b\int_{R^{N}}|\nabla u|^{2}dx)\triangle u + V(x)u =f(x,u)+g(x), & \,\,\,{\rm for} \, x \in R^N, \\ u(x)\rightarrow0, & \,\, {\rm as}\, |x|\rightarrow\infty,\end{array}\right.$$
(0.1)
14.
Let \(\mathcal Lf(x)=-\Delta f (x)+V(x)f(x)\), V?≥?0, \(V\in L^1_{loc}(\mathbb R^d)\), be a non-negative self-adjoint Schrödinger operator on \(\mathbb R^d\). We say that an L 1-function f is an element of the Hardy space \(H^1_{\mathcal L}\) if the maximal functionbelongs to \(L^1(\mathbb R^d)\). We prove that under certain assumptions on V the space \(H^1_{\mathcal L}\) is also characterized by the Riesz transforms \(R_j=\frac{\partial}{\partial x_j}\mathcal L^{-1\slash 2}\), j?=?1,...,d, associated with \(\mathcal L\). As an example of such a potential V one can take any V?≥?0, \(V\in L^1_{loc}\), in one dimension.
相似文献
$ \mathcal M_{\mathcal L} f(x)=\sup\limits_{t>0}|e^{-t\mathcal L} f(x)| $
15.
H. M. Hayrapetyan M. S. Hayrapetyan 《Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)》2008,43(2):85-99
The paper studies a Hilbert boundary value problem in L 1(ρ), where ρ(t) = |1–t|α and α is a real number. For α > ?1, it is proved that the homogeneous problem has n + κ linearly independent solutions when n + κ ≥ 0, where a(t) is the coefficient of the problem, besides, κ ind a(t) and n = [α] + 1 if α is not an integer, and n = α if α is an integer. Conditions under which the problem is solvable are found for the case when α > ?1 and n+κ < 0. For α ≤ ?1 the number of linearly independent solutions of the homogeneous problem depends on the behavior of the function a(t) at the point t = 1. 相似文献
16.
Tao Feng 《Designs, Codes and Cryptography》2009,51(2):175-194
Let D be a (v, k, λ)-difference set in an abelian group G, and (v, 31) = 1. If n = 5p
r
with p a prime not dividing v and r a positive integer, then p is a multiplier of D. In the case 31|v, we get restrictions on the parameters of such difference sets D for which p may not be a multiplier.
相似文献
17.
Iwo Labuda 《Positivity》2010,14(4):801-813
Let μ be a measure from a σ-algebra of subsets of a set T into a sequentially complete Hausdorff topological vector space X. Assume that μ is convexly bounded, i.e., the convex hull of its range is bounded in X, and denote by L
1(μ) the space of scalar valued functions on T which are integrable with respect to the vector measure μ. We study the inheritance of some properties from X to L
1(μ). We show that the bounded multiplier property passes from X to L
1(μ). Answering a 1972 problem of Erik Thomas, we show that for a rather large class of F-spaces X the non-containment of c
0 passes from X to L
1(μ). 相似文献
18.
The matrix Schrödinger operator with point interactions on the semiaxis is studied. Using the theory of boundary triplets and the corresponding Weyl functions, we establish a relationship between the spectral properties (deficiency indices, self-adjointness, semiboundedness, etc.) of the operators under study and block Jacobi matrices of certain class. 相似文献
19.
The one-dimensional Schrödinger operator H X,α with δ-interactions on a discrete set is studied in the framework of the extension theory. Applying the technique of boundary triplets and the corresponding Weyl functions, we establish a connection of these operators with a certain class of Jacobi matrices. The discovered connection enables us to obtain conditions for the self-adjointness, lower semiboundedness, discreteness of the spectrum, and discreteness of the negative part of the spectrum of the operator H X,α . 相似文献
20.
Let M
m
be a m-dimensional submanifold in the n-dimensional unit sphere S
n
without umbilic point. Two basic invariants of M
m
under the M?bius transformation group of S
n
are a 1-form Φ called M?bius form and a symmetric (0,2) tensor A called Blaschke tensor. In this paper, we prove the following rigidity theorem: Let M
m
be a m-dimensional (m≥3) submanifold with vanishing M?bius form and with constant M?bius scalar curvature R in S
n
, denote the trace-free Blaschke tensor by . If , then either ||?||≡0 and M
m
is M?bius equivalent to a minimal submanifold with constant scalar curvature in S
n
; or and M
m
is M?bius equivalent to in for some c≥0 and .
Received: 15 May 2002 / Revised version: 3 February 2003
Published online: 19 May 2003
RID="*"
ID="*" Partially supported by grants of CSC, NSFC and Outstanding Youth Foundation of Henan, China.
RID="†"
ID="†" Partially supported by the Alexander Humboldt von Stiftung and Zhongdian grant of NSFC.
Mathematics Subject Classification (2000): Primary 53A30; Secondary 53B25 相似文献