首页 | 本学科首页   官方微博 | 高级检索  
相似文献
 共查询到20条相似文献,搜索用时 15 毫秒
1.
We study the weighted composition operators Wh,on Hardy space H2(B) whenever h ∈ BMOA(resp.h ∈ VMOA).Analogous results are given for Hp(B) spaces and the scale of weighted Bergman spaces.In the latter case,BMOA is replaced by the Bloch space(resp.VMOA by the little Bloch space).  相似文献   

2.
Let ψ and φ be analytic functions on the open unit disk $\mathbb{D}$ with φ( $\mathbb{D}$ ) ? $\mathbb{D}$ . We give new characterizations of the bounded and compact weighted composition operators W ψ,? from the Hardy spaces H p , 1 ≤ p ≤ ∞, the Bloch space B, the weighted Bergman spaces A α p , α > ? 1,1 ≤ p < ∞, and the Dirichlet space $\mathcal{D}$ to the Bloch space in terms of boundedness (respectively, convergence to 0) of the Bloch norms of W ψ,? f for suitable collections of functions f in the respective spaces. We also obtain characterizations of boundedness for H 1 as well as of compactness for H p , 1 ≤ p < ∞, and $\mathcal{D}$ purely in terms of the symbols ψ and φ.  相似文献   

3.
If f is continuous on the interval [a,b], g is Riemann integrable (resp. Lebesgue measurable) on the interval [α,β] and g([α,β])⊂[a,b], then fg is Riemann integrable (resp. measurable) on [α,β]. A well-known fact, on the other hand, states that fg might not be Riemann integrable (resp. measurable) when f is Riemann integrable (resp. measurable) and g is continuous. If c stands for the continuum, in this paper we construct a c2-dimensional space V and a c-dimensional space W of, respectively, Riemann integrable functions and continuous functions such that, for every fV?{0} and gW?{0}, fg is not Riemann integrable, showing that nice properties (such as continuity or Riemann integrability) can be lost, in a linear fashion, via the composite function. Similarly we construct a c-dimensional space W of continuous functions such that for every gW?{0} there exists a c-dimensional space V of measurable functions such that fg is not measurable for all fV?{0}.  相似文献   

4.
In this article we study the (small) Hankel operator hb on the Hardy and Bergman spaces on a smoothly bounded convex domain of finite type in ℂn. We completely characterize the Hankel operators hb that are bounded, compact, and belong to the Schatten ideal Sp, for 0 < p < ∞. In particular, if hb denotes the Hankel operator on the Hardy space H2 (Ω), we prove that hb is bounded if and only if b ∈ BMOA, compact if and only if b ∈ VMOA, and in the Schatten class if and only if b ∈e Bp, 0 < p < ∞. This last result extends the analog theorem in the case of the unit disc of Peller [19] and Semmes [21]. In order to characterize the bounded Hankel operators, we prove a factorization theorem for functions in H1 (Ω), a result that is of independent interest.  相似文献   

5.
Let X be a rearrangement invariant function space on [0,1]. We consider the Rademacher multiplicator space Λ(R,X) of all measurable functions x such that xhX for every a.e. converging series h=∑anrnX, where (rn) are the Rademacher functions. We study the situation when Λ(R,X) is a rearrangement invariant space different from L. Particular attention is given to the case when X is an interpolation space between the Lorentz space Λ(φ) and the Marcinkiewicz space M(φ). Consequences are derived regarding the behaviour of partial sums and tails of Rademacher series in function spaces.  相似文献   

6.
If XY are two classes of analytic functions in the unit disk D and θ is an inner function, θ is said to be (X,Y)-improving, if every function fX satisfying fθY must actually satisfy fθX. This notion has been recently introduced by K.M. Dyakonov. In this paper we study the (X,Y)-improving inner functions for several pairs of spaces (X,Y). In particular, we prove that for any p∈(0,1) the (Qp,BMOA)-improving inner functions and the (Qp,B)-improving inner functions are precisely the inner functions which belong to the space Qp. Here, B is the Bloch space. We also improve some results of Dyakonov on the subject regarding Lipschitz spaces and Besov spaces.  相似文献   

7.
Whenϕ is an analytic map of the unit diskU into itself, andX is a Banach space of analytic functions onU, define the composition operatorC ϕ byC ϕ (f)=f o ϕ, forfX. In this paper we show how to use the Calderón theory of complex interpolation to obtain information on the spectrum ofC ϕ (under suitable hypotheses onϕ) acting on the Bloch spaceB and BMOA, the space of analytic functions in BMO. To do this we first obtain some results on the essential spectral radius and spectrum ofC ϕ on the Bergman spacesA pand Hardy spacesH p,spaces which are connected toB and BMOA by the interpolation relationships [A 1,B] t =A pand [H 1,BMOA] t =H pfor 1=p(1−t).  相似文献   

8.
Given a Hilbert space H, the infinite-dimensional Lorentz/second-order cone K is introduced. For any xH, a spectral decomposition is introduced, and for any function f:RR, we define a corresponding vector-valued function fH(x) on Hilbert space H by applying f to the spectral values of the spectral decomposition of xH with respect to K. We show that this vector-valued function inherits from f the properties of continuity, Lipschitz continuity, differentiability, smoothness, as well as s-semismoothness. These results can be helpful for designing and analyzing solution methods for solving infinite-dimensional second-order cone programs and complementarity problems.  相似文献   

9.
It is shown that if X is a countably paracompact collectionwise normal space, Y is a Banach space and φ:XY2 is a lower semicontinuous mapping such that φ(x) is Y or a compact convex subset with Cardφ(x)>1 for each xX, then φ admits a continuous selection f:XY such that f(x) is not an extreme point of φ(x) for each xX. This is an affirmative answer to the problem posed by V. Gutev, H. Ohta and K. Yamazaki [V. Gutev, H. Ohta and K. Yamazaki, Selections and sandwich-like properties via semi-continuous Banach-valued functions, J. Math. Soc. Japan 55 (2003) 499-521].  相似文献   

10.
We show that the Libera operator, L, on some spaces of analytic functions is a continuous extension of the conjugate of the Cesàro operator. Results on L acting on various spaces are obtained. In particular, L maps the Bloch space into BMOA. We also prove some results on the best approximation by polynomials in Hardy and Bergman spaces.  相似文献   

11.
12.
W-Sobolev spaces     
Fix strictly increasing right continuous functions with left limits and periodic increments, Wi:RR, i=1,…,d, and let for xRd. We construct the W-Sobolev spaces, which consist of functions f having weak generalized gradients ∇Wf=(W1f,…,Wdf). Several properties, that are analogous to classical results on Sobolev spaces, are obtained. Existence and uniqueness results for W-generalized elliptic equations, and uniqueness results for W-generalized parabolic equations are also established. Finally, an application of this theory to stochastic homogenization is presented.  相似文献   

13.
Let δa be the Dirac delta function at aR and (E)⊂(L2)⊂(E) the canonical framework of white noise analysis over white noise space (E,μ), where E=S(R). For hH=L2(R) with h≠0, denote by Mh the operator of multiplication by Wh=〈⋅,h〉 in (L2). In this paper, we first show that Mh is δa-composable. Thus the delta function δa(Mh) makes sense as a generalized operator, i.e. a continuous linear operator from (E) to (E). We then establish a formula showing an intimate connection between δa(Mh) as a generalized operator and δa(Wh) as a generalized functional. We also obtain the representation of δa(Mh) as a series of integral kernel operators. Finally we prove that δa(Mh) depends continuously on aR.  相似文献   

14.
This paper deals with the boundedness and compactness of the weighted composition operators from the F(p, q, s) spaces, including Hardy space, Bergman space, Qp space, BMOA space, Besov space and α-Bloch space, to Bers-type spaces Hv^∞( or little Bers-type spaces Hv,o∞ ), where v is normal.  相似文献   

15.
New function spaces, which generalize the classical Dirichlet space, BMOA or also the recently defined Q p space, are introduced on Riemann surfaces. Except inclusions between these generalized spaces it is shown that the capacity Bloch space is a maximal space for them.  相似文献   

16.
Compactness of composition operators on BMOA and VMOA   总被引:1,自引:0,他引:1  
We give a new and simple compactness condition for composition operators on BMOA,the space of all analytic functions of the bounded mean oscillation on the unit disk.Using our results one may immediately obtain that compactness of a composition operator on BMOA implies its compactness on the Bloch space as well as on the Hardy space.Similar results on VMOA are also given.  相似文献   

17.
For 0<p<+∞ let hp be the harmonic Hardy space and let bp be the harmonic Bergman space of harmonic functions on the open unit disk U. Given 1?p<+∞, denote by ‖⋅bp and ‖⋅hp the norms in the spaces bp and hp, respectively. In this paper, we establish the harmonic hp-analogue of the known isoperimetric type inequality ‖fb2p?‖fhp, where f is an arbitrary holomorphic function in the classical Hardy space Hp. We prove that for arbitrary p>1, every function fhp satisfies the inequality
fb2p?apfhp,  相似文献   

18.
We prove the existence of solutions of the Cauchy problem for the doubly nonlinear evolution equation: dv(t)/dt+Vφt(u(t))∋f(t), v(t)∈Hψ(u(t)), 0<t<T, where Hψ (respectively, Vφt) denotes the subdifferential operator of a proper lower semicontinuous functional ψ (respectively, φt explicitly depending on t) from a Hilbert space H (respectively, reflexive Banach space V) into (−∞,+∞] and f is given. To do so, we suppose that V?HH?V compactly and densely, and we also assume smoothness in t, boundedness and coercivity of φt in an appropriate sense, but use neither strong monotonicity nor boundedness of Hψ. The method of our proof relies on approximation problems in H and a couple of energy inequalities. We also treat the initial-boundary value problem of a non-autonomous degenerate elliptic-parabolic problem.  相似文献   

19.
A weighted composition operator Cψ,φ takes an analytic map f on the open unit disc of the complex plane to the analytic map ψf°φ where φ is an analytic map of the open unit disc into itself and ψ is an analytic map on the open unit disc. This paper studies the invertibility of such operators. The two maps ψ and φ are characterized when Cψ,φ acts on the Hardy-Hilbert space of the unit disc H2(D). Depending upon the nature of the fixed points of φ spectra are then investigated.  相似文献   

20.
In this paper we develop the frame theory of subspaces for separable Hilbert spaces. We will show that for every Parseval frame of subspaces {Wi}iI for a Hilbert space H, there exists a Hilbert space KH and an orthonormal basis of subspaces {Ni}iI for K such that Wi=P(Ni), where P is the orthogonal projection of K onto H. We introduce a new definition of atomic resolution of the identity in Hilbert spaces. In particular, we define an atomic resolution operator for an atomic resolution of the identity, which even yield a reconstruction formula.  相似文献   

设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号