共查询到20条相似文献,搜索用时 46 毫秒
1.
Peter L. Polyakov 《Journal of Geometric Analysis》1996,6(2):233-276
We construct integral operatorsR r andH r on the spaces of differential forms of the type (o, r) withr <q on a regularq-concave CR manifoldM such that $$f(z) = \bar \partial _M R_r (f)(z) + R_{r + 1} (\bar \partial _M f)(z) + H_r (f)(z),$$ for a differential formf ∈ L (0,r) s (M) and forz ∈ M′ ?M, whereH r is compact andR r admits sharp estimates. 相似文献
2.
It is shown that the maximal operator of the Fejér means of a tempered distribution is bounded from thed-dimensional Hardy spaceH p (R×···×R) toL p (R d ) (1/2<p<∞) and is of weak type (H 1 ?i ,L 1) (i=1,…,d), where the Hardy spaceH 1 ?i is defined by a hybrid maximal function. As a consequence, we obtain that the Fejér means of a functionf ∈H 1 ?i ?L(logL) d?1 converge a.e. to the function in question. Moreover, we prove that the Fejér means are uniformly bounded onH p (R×···×R) whenever 1/2<p<∞. Thus, in casef ∈H p (R×···×R) the Fejér means converge tof inH p (R×···×R) norm. The same results are proved for the conjugate Fejér means, too. 相似文献
3.
Let Ω be a bounded domain in the plane whose boundary consists of a finite number of disjoint analytic simple closed curves LetA denote the space of analytic functions on Ω which are square integrable over Ω with respect to area measure and letP denote the orthogonal projection ofL 2(Ω,dA) ontoA. A functionb inA induces a Hankel operator (densely defined) onA by the ruleH b (g)=(I?P)bg. This paper continues earlier investigations of the authors and others by determining conditions under whichH b is bounded, compact, or lies in the Schatten-von Neumann idealS p , 1<p<∞ 相似文献
4.
We characterize the additive operators preserving rank-additivity on symmetry matrix spaces. LetS n(F) be the space of alln×n symmetry matrices over a fieldF with 2,3 ∈F *, thenT is an additive injective operator preserving rank-additivity onS n(F) if and only if there exists an invertible matrixU∈M n(F) and an injective field homomorphism ? ofF to itself such thatT(X)=cUX ?UT, ?X=(xij)∈Sn(F) wherec∈F *,X ?=(?(x ij)). As applications, we determine the additive operators preserving minus-order onS n(F) over the fieldF. 相似文献
5.
Our aim in this note is to deal with boundary limits of monotone Sobolev functions with ▽u∈ Lp(·)logLq(·)(B) for the unit ball BRn. Here p(·) and q(·) are variable exponents satisfyingthe log-Hlder and the log log-Hlder conditions, respectively. 相似文献
6.
A non-zero vector-valued sequence u ∈ ?q(X′) is a cover for a subset M of ?P(X) if, for some 0 < α ≤ 1, ∥u * h∥ ∞ ≥ α ∥u∥q ∥h∥p for all h ∈ M. Covers of ?1 = ?1(R) are important in worst case system identification in ?1 and in the reconstruction of elements in a normed space from corrupted functional values. We investigate the existence of covers for certain naturally occurring subspaces of ?p(X). We show that there exist finitely supported covers for some subspaces, and obtain lower bounds for their ’lengths’. We also obtain similar results for covers associated with convolution products for spaces of measurable vector-valued functions defined on the positive real axis. 相似文献
7.
Shi Hongjian 《分析论及其应用》1989,5(1):87-96
Let N denote the Hardy-Littlewood maximal operator for the familyR of one parameter rectangles. In this paper, we obtain that for 1 w p (lr) to L W P (lr) if and only if w ∈ AP(R); for 1≤p<∞, N is bounded from L W P (lr) to weak L W P (lr) if and only if W ∈ AP(R). Here we say W∈Ap (1), if $$\begin{gathered} \mathop {sup}\limits_{R \in R} \left( {\tfrac{1}{{|R|}}\smallint _r wdx} \right)\left( {\tfrac{1}{{|R|}}\smallint _R w^{ - 1/(p - 1)} dx} \right)^{p - 1}< \infty ,1< p< \infty , \hfill \\ (Nw)(x) \leqslant Cw(x)a.e.,p = 1 \hfill \\ \end{gathered} $$ , 相似文献
8.
LetR be a ring. For the setF of all nonzero ideals ofR, we introduce an equivalence relation inF as follows: For idealsI andJ, I~J if and only ifV R (I)=V R(J), whereV R() is the centralizer inR. LetI R=F/~. Then we can see thatn(I R), the cardinality ofI R, is 1 if and only ifR is either a prime ring or a commutative ring (Theorem 1.1). An idealI ofR is said to be a commutator ideal ifI is generated by{st?ts; s∈S, t∈T} for subsetS andT ofR, andR is said to be a ring with (N) if any commutator ideal contains no nonzero nilpotent ideals. Then we have the following main theorem: LetR be a ring with (N). Thenn(I R) is finite if and only ifR is isomorphic to an irredundant subdirect sum ofS⊕Z whereS is a finite direct sum of non commutative prime rings andZ is a commutative ring (Theorem 2.1). Finally, we show that the existence of a ringR such thatn(I R)=m for any given natural numberm. 相似文献
9.
P. K. Chaurasia 《Analysis Mathematica》2009,35(1):15-35
Let G denote a locally compact abelian group and H a separable Hilbert space. Let L p (G, H), 1 ≤ p < ∞, be the space of H-valued measurable functions which are in the usual L p space. Motivated by the work of Helgason [1], Figa-Talamanca [11] and Bachelis [2, 3], we have defined the derived space of the Banach space L p (G, H) and have studied its properties. Similar to the scalar case, we prove that if G is a noncompact, locally compact abelian group, then L p 0 (G, H) = {0} holds for 1 ≤ p < 2. Let G be a compact abelian group and Γ be its dual group. Let S p (G, H) be the L 1(G) Banach module of functions in L p (G, H) having unconditionally convergent Fourier series in L p -norm. We show that S p (G, H) coincides with the derived space L p 0 (G, H), as in the scalar valued case. We also show that if G is compact and abelian, then L p 0 (G, H) = L 2(G, H) holds for 1 ≤ p ≤ 2. Thus, if F ∈ L p (G, H), 1 ≤ p < 2 and F has an unconditionally convergent Fourier series in L p -norm, then F ∈ L 2(G, H). Let Ω be the set of all functions on Γ taking only the values 1, ?1 and Ω* be the set of all complex-valued functions on Γ having absolute value 1. As an application of the derived space L p 0 (G, H), we prove the following main result of this paper. Let G be a compact abelian group and F be an H-valued function on the dual group Γ such that $$ \sum \omega (\gamma )F(\gamma )\gamma $$ is a Fourier-Stieltjes series of some measure µ ∈ M(G, H) for every scalar function ω such that |ω(γ)| = 1. Then F ∈ l 2(Γ, H). 相似文献
10.
Esistono un gruppo compatto non commutativoG ~ ed un operatore di convoluzioneT tale che: perp∈[2,4] e perq∈[1,2),T∈L p p (G ~) eT?L q q (G ~). 相似文献
11.
12.
G. C. Kyriazis 《Constructive Approximation》1995,11(2):141-164
We give sufficient conditions on a single function ? so that the principal shift-invariant space generated by ? provides a prescribed order of approximation inL p (R d ), 1<p<∞, and inH p (R d ), 0<p≤1. In particular, our conditions are given in terms of $\hat \varphi$ and are satisfied even when ? does not decay quickly at infinity. 相似文献
13.
In this article we investigate the analysis of a finite element method for solving H(curl; ??)-elliptic interface problems in general three-dimensional polyhedral domains with smooth interfaces. The continuous problems are discretized by means of the first family of lowest order Nédélec H(curl; ??)-conforming finite elements on a family of tetrahedral meshes which resolve the smooth interface in the sense of sufficient approximation in terms of a parameter ?? that quantifies the mismatch between the smooth interface and the triangulation. Optimal error estimates in the H(curl; ??)-norm are obtained for the first time. The analysis is based on a ??-strip argument, a new extension theorem for H 1(curl; ??)-functions across smooth interfaces, a novel non-standard interface-aware interpolation operator, and a perturbation argument for degrees of freedom for H(curl; ??)-conforming finite elements. Numerical tests are presented to verify the theoretical predictions and confirm the optimal order convergence of the numerical solution. 相似文献
14.
Meng-Kiat Chuah 《Journal of Geometric Analysis》2000,10(2):257-267
Consider the complex torus T C under the natural action of the compact real torus T. In this paper, we study T-invariant Kähler structures ω on TC. For each ω, we consider the corresponding line bundleL on T C. Namely, the Chern class ofL is [ω], and L is equipped with a connection ? whose curvature is ω. We construct a canonical T-invariant L 2-structure on the sections ofL,and let H ω be the square-integrable holomorphic sections ofL.Then the Hilbert space H ω is a unitary T-representation, and we study the multiplicity of the (l-dimensional) irreducible unitary T-representations in Hω. We shall see that the multiplicity is controlled by the image of the moment map corresponding to the T-action preserving ω. 相似文献
15.
Hai-yan Wu Chong-guang Cao Wei Zhang 《Journal of Applied Mathematics and Computing》2008,26(1-2):475-487
Suppose F is a field of characteristic not 2. Let n and m be two arbitrary positive integers with n≥2. We denote by M n (F) and S n (F) the space of n×n full matrices and the space of n×n symmetric matrices over F, respectively. All linear maps from S n (F) to M m (F) preserving M–P inverses of matrices are characterized first, and thereby all linear maps from S n (F) (M n (F)) to S m (F) (M m (F)) preserving M–P inverses of matrices are characterized, respectively. 相似文献
16.
Alano Ancona 《Arkiv f?r Matematik》1995,33(1):1-44
Letf:V→R be a function defined on a subsetV ofR n ×R d let?:x→inf{f(x t);t such that(x t)∈V} denote theshadow off and letΦ={(x t)∈V; f(x t)=?(x)} This paper deals with the characterization of some properties of ? in terms of the infinitesimal behavior off near points ζ∈Φ proving in particular a conjecture of J M Trépreau concerning the cased=1 Characterizations of this type are provided for the convexity the subharmonicity or theC 1 1 regularity of ? in the interior ofI={x∈ R n;εR d (x t)∈V} and in theC 1 1 case an expression forD 2? is given To some extent an answer is given to the following question: which convex function ?:I→R I interval ?R (resp which function √:I→R of classC 1 1) is the shadow of aC 2 functionf:I×R→R? 相似文献
17.
Paul Thurston 《Journal of Geometric Analysis》1996,6(3):475-494
The concepts of geometric and topological tame point are introduced for a space of nonpositive curvature. These concepts are applied to the characterization problem forCAT(0) 4-manifolds. It is shown that everyCAT(0)M 4 having a single (geometric or topological) tame point is homeomorphic toR 4. Davis and Januszkiewicz have recently constructedCAT(0)n-manifolds,M n withn ≥ 5 such that the set of tame points form a dense open subset ofM n , butM n ≠R n . 相似文献
18.
Lin YU 《数学学报(英文版)》2014,30(8):1365-1380
The dual of B-valued martingale Hardy space Hs(p)r(B) with small index 0 r ≤ 1,which is associated with the conditional p-variation of B-valued martingale,is characterized.In order to obtain the results,a new type of Campanato spaces for B-valued martingales is introduced and the classical technique of atomic decompositions is improved.Some results obtained here are connected closely with the p-uniform smoothness and q-uniform convexity of the underlying Banach space. 相似文献
19.
20.
REIDER Igor 《中国科学 数学(英文版)》2013,56(1):1-42
The nonabelian Jacobian J(X;L,d) of a smooth projective surface X is inspired by the classical theory of Jacobian of curves.It is built as a natural scheme interpolating between the Hilbert scheme X [d] of subschemes of length d of X and the stack M X(2,L,d) of torsion free sheaves of rank 2 on X having the determinant OX(L) and the second Chern class(= number) d.It relates to such influential ideas as variations of Hodge structures,period maps,nonabelian Hodge theory,Homological mirror symmetry,perverse sheaves,geometric Langlands program.These relations manifest themselves by the appearance of the following structures on J(X;L,d):1) a sheaf of reductive Lie algebras;2)(singular) Fano toric varieties whose hyperplane sections are(singular) Calabi-Yau varieties;3) trivalent graphs.This is an expository paper giving an account of most of the main properties of J(X;L,d) uncovered in Reider 2006 and ArXiv:1103.4794v1. 相似文献