共查询到20条相似文献,搜索用时 0 毫秒
1.
The composition operators on weighted Bloch space 总被引:9,自引:0,他引:9
R. Yoneda 《Archiv der Mathematik》2002,78(4):310-317
We will characterize the boundedness and compactness of the composition operators on weighted Bloch space B log = { f ? H(D): supz ? D (1-| z|2) ( log\frac21-| z|2 )| f¢(z)| B_{ \log }= \{ f \in H(D): \sup_{z \in D } (1-\left| z\right|^2) \left( \log \frac{2}{1-\left| z\right|^2} \right)\left| f'(z)\right| < +¥} +\infty \} , where H(D) be the class of all analytic functions on D. 相似文献
2.
We characterize boundedness and compactness of products of differentiation operators and weighted composition operators between weighted Banach spaces of analytic functions and weighted Zygmund spaces or weighted Bloch spaces with general weights. 相似文献
3.
In this paper, we give some estimates for the essential norm and a new characterization for the boundedness and compactness of weighted composition operators from weighted Bergman spaces and Hardy spaces to the Bloch space. 相似文献
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5.
Lanzhe Liu 《Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)》2010,45(3):136-150
The paper proves some weighted boundedness for the multilinear operators related to some pseudo-differential operators on the generalized Morrey spaces by using the sharp function estimate of the multilinear operators. 相似文献
6.
Eva A. Gallardo-Gutiérrez Jonathan R. Partington 《Journal of Functional Analysis》2010,258(11):3593-3603
Boundedness (resp. compactness) of weighted composition operators Wh,φ acting on the classical Hardy space H2 as Wh,φf=h(f○φ) are characterized in terms of a Nevanlinna counting function associated to the symbols h and φ whenever h∈BMOA (resp. h∈VMOA). Analogous results are given for Hp 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
7.
Songxiao Li 《Journal of Mathematical Analysis and Applications》2012,394(2):706-711
The boundedness and compactness of the differences of two generalized composition operators on the Bloch space in the unit disk are investigated in this paper. 相似文献
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9.
S. M. Farsani 《Siberian Mathematical Journal》2013,54(2):368-378
Let α ∈ (0, 1). Consider the Riemann-Liouville fractional operator of the form $f \to T_\alpha f(x): = v(x)\int\limits_0^x {\frac{{f(y)u(y)dy}} {{(x - y)^{1 - \alpha } }}} ,x > 0, $ with locally integrable weight functions u and v. We find criteria for the L p → L q -boundedness and compactness of T α when 0 < p,q < ∞, p > 1/α under the condition that u monotonely decreases on ?+:= [0,∞). The dual versions of this result are given. 相似文献
10.
Compact composition operators on the Bloch space in polydiscs 总被引:1,自引:0,他引:1
Let Un be the unit polydisc of ℂn and φ=(φ1, ⋯, φ
n
) a holomorphic self-map of Un. As the main result of the paper, it shows that the composition operator C is compact on the Bloch space β(Un) if and only if for every ε > 0, there exists a δ > 0, such that
whenever dist(φ(z), ∂U
n
)<δ. 相似文献
11.
Gajath Gunatillake 《Proceedings of the American Mathematical Society》2008,136(8):2895-2899
A weighted composition operator takes an analytic map on the open unit disk of the complex plane to the analytic map , where is an analytic map of the open unit disk into itself and is an analytic map on the open unit disk. This paper studies how the compactness of depends on the interaction between the two maps and .
12.
Anuradha Gupta 《复变函数与椭圆型方程》2020,65(9):1488-1500
13.
We investigate isometric composition operators on the weighted Dirichlet space \({D_\alpha }\) with standard weights \({(1 - {\left| z \right|^2})^\alpha },\alpha > - 1\). The main technique used comes from Martín and Vukoti? who completely characterized the isometric composition operators on the classical Dirichlet space D. We solve some of these but not in general. We also investigate the situation when \({D_\alpha }\) is equipped with another equivalent norm. 相似文献
14.
This paper gives a note on weighted composition operators on the weighted Bergman space, which shows that for a fixed composition symbol, the weighted composition operators are bounded on the weighted Bergman space only with bounded weighted symbols if and only if the composition symbol is a finite Blaschke product. 相似文献
15.
Pratibha Ghatage Dechao Zheng Nina Zorboska 《Proceedings of the American Mathematical Society》2005,133(5):1371-1377
We give a necessary and sufficient condition for a composition operator on the Bloch space to have closed range. We show that when is univalent, it is sufficient to consider the action of on the set of Möbius transforms. In this case the closed range property is equivalent to a specific sampling set satisfying the reverse Carleson condition.
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18.
If and are linear operators acting between Banach spaces, we show that compactness of relative to does not in general imply that has -bound zero. We do, however, give conditions under which the above implication is valid.
19.
Let ϕ and ψ be holomorphic self-maps of the unit disk, and denote by C
ϕ
, C
ψ
the induced composition operators. This paper gives some simple estimates of the essential norm for the difference of composition
operators C
ϕ
−C
ψ
from Bloch spaces to Bloch spaces in the unit disk. Compactness of the difference is also characterized. 相似文献
20.
Manuel D. Contreras Santiago Díaz-Madrigal Dragan Vukotić 《Journal of Mathematical Analysis and Applications》2014
We obtain exhaustive results and treat in a unified way the question of boundedness, compactness, and weak compactness of composition operators from the Bloch space into any space from a large family of conformally invariant spaces that includes the classical spaces like BMOA , Qα, and analytic Besov spaces Bp. In particular, by combining techniques from both complex and functional analysis, we prove that in this setting weak compactness is equivalent to compactness. For the operators into the corresponding “small” spaces we also characterize the boundedness and show that it is equivalent to compactness. 相似文献