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1.
For α satisfying 0 < α < π, suppose that C
1 and C
2 are rays from the origin, C
1: z = re
i(π−α) and C
2: z = re
i(π+α), r ≥ 0, and that D = {z: | arg z − π| < α}. Let u be a nonconstant subharmonic function in the plane and define B(r, u) = sup|z|=r
u(z) and A
D
(r, u) = $
\inf _{z \in \bar D_r }
$
\inf _{z \in \bar D_r }
u(z), where D
r
= {z: z ∈ D and |z| = r}. If u(z) = (1 + o(1))B(|z|, u) as z → ∞ on C
1 ∪ C
2 and A
D
(r, u) = o(B(r, u)) as r → ∞, then the lower order of u is at least π/(2α). 相似文献
2.
Pascale Vitse 《Rendiconti del Circolo Matematico di Palermo》2004,53(2):283-312
For Banach space operatorsT satisfying the Tadmor-Ritt condition ‖(zI−T)−1‖≤C|z−1|−1, |z|>1, we show how to use the Riesz turndown collar theorem to estimate sup
n≥0‖T
n‖. A similar estimate is shown for lim sup
n
‖T
n‖ in terms of the Ritt constantM=lim sup
z→1‖(1−z)(zI−T)−1‖. We also obtain an estimate of the functional calculus for these operators proving, in particular, that ‖f(T)‖≤C
q‖f‖
Mult
, where ‖·‖
Mult
stands for the multiplier norm of the Cauchy-Stieltjes integrals over a Lusin type cone domain depending onC and a parameterq, 0<q<1.
Notation.D denotes the open unit disc of the complex plane,D={z∈ℂ:|z|<1}, andT={z∈ℂ:|z|=1} is the unit circle.H
∞ is the Banach algebra of bounded analytic functions onD equipped with the supremum norm ‖.‖∞. 相似文献
3.
V. G. Petrosyan 《Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)》2011,46(6):305-312
The paper studies the rotation of the image of the sphere |z| = r under mappings by functions of the form w(z) − p(z), where w(z) is an entire meromorphic function, while p(z) is a polynomial. In terms of rotations, some analogs of the Nevanlinna Second Fundamental Theorem are established. 相似文献
4.
Baode Li Yinsheng Jiang Hui Cao 《分析论及其应用》2007,23(2):138-146
In the paper we obtain vector-valued inequalities for Calderon-Zygmund operator,simply CZO On Herz space and weak Herz space.In particular,we obtain vector-valued inequalities for CZO on Lq(Rd,│x│αdμ)space,with 1<q<∞,-n<α<n(q-1),and on L1,∞(Rd,│x│αdμ)space,with -n<α<0. 相似文献
5.
Xiao Jie 《数学学报(英文版)》1994,10(2):192-201
LetD={z∈Σ:|z|<1} and ϕ be a normal function on [0,1). Forp∈(0,1) such a function ϕ is used to define a Bergman spaceA
p
(ϕ) onD with weight ϕ
p
(|·|)/(1-|·|2). In this paper, the dual space ofA
p
(ϕ) is given, four characteristics of Carleson measure onA
p
(ϕ) are obtained. Moreover, as an application, three sequence interpolation theorems inA
p
(ϕ) are derived.
Supported by the Doctoral Program Foundation of Institute of Higher Education, P.R. China. 相似文献
6.
Oscar F. Bandtlow 《Integral Equations and Operator Theory》2008,61(1):21-43
For a, α > 0 let E(a, α) be the set of all compact operators A on a separable Hilbert space such that s
n
(A) = O(exp(-anα)), where s
n
(A) denotes the n-th singular number of A. We provide upper bounds for the norm of the resolvent (zI − A)−1 of A in terms of a quantity describing the departure from normality of A and the distance of z to the spectrum of A. As a consequence we obtain upper bounds for the Hausdorff distance of the spectra of two operators in E(a, α).
相似文献
7.
The singular integral operator J Ω,α, and the Marcinkiewicz integral operator (~μ)Ω,α are studied. The kernels of the operators behave like |y|-n-α(α>0) near the origin, and contain an oscillating factor ei|y|-β(β>0) and a distribution Ω on the unit sphere Sn-1 It is proved that, if Ω is in the Hardy space Hr (Sn-1) with 0<r= (n-1)/(n-1 )(>0), and satisfies certain cancellation condition,then J Ω,α and uΩ,α extend the bounded operator from Sobolev space Lpγ to Lebesgue space Lp for some p. The result improves and extends some known results. 相似文献
8.
Let S ⊂ ℜn+1
be the graph of the function ϕ :[−1, 1]
n → ℜ defined by ϕ (x
1
, …, xn) = ∑
j=1
n
|xj|αj, with1<α
1
≤ … ≤ αn, let σ the Euclidean area measure on S. In this article we study the Lp − Lq boundedness of convolution operators with the singular Borel measure on Rn+1
given by μ (E)=σ (E ∩ S) 相似文献
9.
Consider a bounded planar domain D, an instance h of the Gaussian free field on D, with Dirichlet energy (2π)−1∫
D
∇h(z)⋅∇h(z)dz, and a constant 0≤γ<2. The Liouville quantum gravity measure on D is the weak limit as ε→0 of the measures
eg2/2 eghe(z)dz,\varepsilon^{\gamma^2/2} e^{\gamma h_\varepsilon(z)}dz, 相似文献
10.
Petros Galanopoulos Daniel Girela Rodrigo Hernández 《Journal of Geometric Analysis》2011,21(3):665-682
This paper is concerned mainly with the logarithmic Bloch space ℬlog which consists of those functions f which are analytic in the unit disc
\mathbbD{\mathbb{D}} and satisfy
sup|z| < 1(1-|z|)log\frac11-|z||f¢(z)| < ¥\sup_{\vert z\vert <1}(1-\vert z\vert )\log\frac{1}{1-\vert z\vert}\vert f^{\prime}(z)\vert <\infty , and the analytic Besov spaces B
p
, 1≤p<∞. They are all subspaces of the space VMOA. We study the relation between these spaces, paying special attention to the membership of univalent functions in them. We
give explicit examples of:
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