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1.
The author establishes some geometric criteria for a Haj?asz-Sobolev -extension (resp. -imbedding) domain of Rn with n?2, s∈(0,1] and p∈[n/s,∞] (resp. p∈(n/s,∞]). In particular, the author proves that a bounded finitely connected planar domain Ω is a weak α-cigar domain with α∈(0,1) if and only if for some/all s∈[α,1) and p=(2−α)/(sα), where denotes the restriction of the Triebel-Lizorkin space on Ω.  相似文献   

2.
Let be a positive integer, let F be a family of meromorphic functions in a domain D, all of whose zeros have multiplicity at least k+1, and let , be two holomorphic functions on D. If, for each fF, f=a(z)⇔f(k)=h(z), then F is normal in D.  相似文献   

3.
Let C be a closed convex subset of a uniformly smooth Banach space E and let T:CC be a nonexpansive mapping with a nonempty fixed points set. Given a point uC, the initial guess x0C is chosen arbitrarily and given sequences , and in (0,1), the following conditions are satisfied:
(i)
;
(ii)
αn→0, βn→0 and 0<a?γn, for some a∈(0,1);
(iii)
, and . Let be a composite iteration process defined by
  相似文献   

4.
In this paper, the authors prove that Besov-Morrey spaces are proper subspaces of Besov-type spaces and that Triebel-Lizorkin-Morrey spaces are special cases of Triebel-Lizorkin-type spaces . The authors also establish an equivalent characterization of when τ∈[0,1/p). These Besov-type spaces and Triebel-Lizorkin-type spaces were recently introduced to connect Besov spaces and Triebel-Lizorkin spaces with Q spaces. Moreover, for the spaces and , the authors investigate their trace properties and the boundedness of the pseudo-differential operators with homogeneous symbols in these spaces, which generalize the corresponding classical results of Jawerth and Grafakos-Torres by taking τ=0.  相似文献   

5.
Let p∈(1,∞), q∈[1,∞), sR and . In this paper, the authors establish the φ-transform characterizations of Besov-Hausdorff spaces and Triebel-Lizorkin-Hausdorff spaces (q>1); as applications, the authors then establish their embedding properties (which on is also sharp), smooth atomic and molecular decomposition characterizations for suitable τ. Moreover, using their atomic and molecular decomposition characterizations, the authors investigate the trace properties and the boundedness of pseudo-differential operators with homogeneous symbols in and (q>1), which generalize the corresponding classical results on homogeneous Besov and Triebel-Lizorkin spaces when p∈(1,∞) and q∈[1,∞) by taking τ=0.  相似文献   

6.
Let ?A be a normal completely positive map on B(H) with Kraus operators . Denote M the subset of normal completely positive maps by . In this note, the relations between the fixed points of ?A and are investigated. We obtain that , where K(H) is the set of all compact operators on H and is the dual of ?AM. In addition, we show that the map is a bijection on M.  相似文献   

7.
We consider a process given by the SDE , t∈[0,T), with initial condition , where T∈(0,∞], αR, (Bt)t∈[0,T) is a standard Wiener process, b:[0,T)→R?{0} and σ:[0,T)→(0,∞) are continuously differentiable functions. Assuming , t∈[0,T), with some KR, we derive an explicit formula for the joint Laplace transform of and for all t∈[0,T) and for all αR. Our motivation is that the maximum likelihood estimator (MLE) of α can be expressed in terms of these random variables. As an application, we show that in case of α=K, K≠0,
  相似文献   

8.
Let be a strictly stationary sequence of positively associated random variables with mean zero and finite variance. Set , Mn=maxk?n|Sk|, n?1. Suppose . In this paper, we study the exact convergence rates of a kind of weighted infinite series of , and as ε↘0, respectively.  相似文献   

9.
This paper is concerned with the well-posedness of the Navier-Stokes-Nerst-Planck-Poisson system (NSNPP). Let sp=−2+n/p. We prove that the NSNPP has a unique local solution for in a subspace, i.e., VuVvVv1, of with . We also prove that there exists a unique small global solution for any small initial data with .  相似文献   

10.
Let S be a semitopological semigroup. Let C be a closed convex subset of a uniformly convex Banach space E whose norm is Fréchet differentiable and be a continuous representation of S as almost asymptotically nonexpansive type mapping of C into C such that the common fixed point set F(ℑ) of ℑ in C is nonempty. In this paper, we prove that if S is right reversible then for each xC, the closed convex set consists of at most one point. We also prove that if S is reversible, then the intersection is nonempty for each xC if and only if there exists a nonexpansive retraction P of C onto F(ℑ) such that PTt=TtP=P for all tS and Px is in the closed convex hull of for each xC.  相似文献   

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