首页 | 本学科首页   官方微博 | 高级检索  
相似文献
 共查询到10条相似文献,搜索用时 125 毫秒
1.
Let Un be the unit polydisc of Cn and φ= (φ1,...,φn? a holomorphic self-map of Un. Let 0≤α< 1. This paper shows that the composition operator Cφ, is bounded on the Lipschitz space Lipa(Un) if and only if there exists M > 0 such thatfor z∈Un. Moreover Cφ is compact on Lipa(Un) if and only if Cφ is bounded on Lipa(Un) and for every ε > 0, there exists a δ > 0 such that whenever dist(φ(z),σUn) <δ  相似文献   

2.
We characterize the composition operators mapping Blochs boundedly into the weighted Bergman spaces of logarithmic weight. For 0 < p < ∞, 1 < α < ∞, let Ap, log α denote the space of holomorphic functions F in the unit disc D for which
and let Ap, log ασ denote the class of holomorphic self maps f of D for which
Then for the Bloch pullback operator Cf, the following are equivalent:
(1)  Cf maps Bloch space boundedly into A2p, log α
(2) 
(3)  .
This work was supported by the Korea Research Foundation Grant funded by the Korean Government (MOEHRD, Basic Research Promotion Fund) (KRF-2007-313-C00026).  相似文献   

3.
Let U n be the unit polydisk in C n and S be the space of functions of regular variation. Let 1 ≤ p < ∞, ω = (ω 1, ..., ω n ), ω j S(1 ≤ jn) and fH(U n ). The function f is said to be in holomorphic Besov space B p (ω) if
$ \left\| f \right\|_{B_p (\omega )}^p = \int_{U^n } {\left| {Df(z)} \right|^p \prod\limits_{j = 1}^n {\frac{{\omega _j (1 - |z_j |)}} {{(1 - |z_j |^{2 - p} )}}} dm_{2n} (z) < + \infty } $ \left\| f \right\|_{B_p (\omega )}^p = \int_{U^n } {\left| {Df(z)} \right|^p \prod\limits_{j = 1}^n {\frac{{\omega _j (1 - |z_j |)}} {{(1 - |z_j |^{2 - p} )}}} dm_{2n} (z) < + \infty }   相似文献   

4.
Let U(λ, μ) denote the class of all normalized analytic functions f in the unit disk |z| < 1 satisfying the condition
$ \frac{{f(z)}} {z} \ne 0and\left| {f'(z)\left( {\frac{z} {{f(z)}}} \right)^{\mu + 1} - 1} \right| < \lambda ,\left| z \right| < 1. $ \frac{{f(z)}} {z} \ne 0and\left| {f'(z)\left( {\frac{z} {{f(z)}}} \right)^{\mu + 1} - 1} \right| < \lambda ,\left| z \right| < 1.   相似文献   

5.
The following regularity of weak solutions of a class of elliptic equations of the form are investigated.  相似文献   

6.
Let and τ denote the invariant gradient and invariant measure on the unit ball B of ℂn, respectively. Assume that f is a holomorphic function on B and ϕ ∈ C2(ℝ) is a nonnegative, nondecreasing, convex function. Then f belongs to the Hardy-Orlicz space H ϕ(B>) if and only if
Analogous characterizations of Bergman-Orlicz spaces are obtained. Bibliography: 9 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 333, 2006, pp. 43–53.  相似文献   

7.
If p(z) is a polynomial of degree n having all its zeros on |z| = k, k ≤ 1, then it is proved[5] that max |z|=1 |p′(z)| ≤ kn1n + kn m|z|=ax1 |p(z)|. In this paper, we generalize the above inequality by extending it to the polar derivative of a polynomial of the type p(z) = cnzn + ∑n j=μ cn jzn j, 1 ≤μ≤ n. We also obtain certain new inequalities concerning the maximum modulus of a polynomial with restricted zeros.  相似文献   

8.
9.
  A theorem from the classical complex analysis proved by Davydov in 1949 is extended to the theory of solution of a special case of the Beltrami equation in the z-complex plane (i.e., null solutions of the differential operator ). It is proved that if γ is a rectifiable Jordan closed curve and f is a continuous complex-valued function on γ such that the integral
converges uniformly on γ as r → 0, where n(ζ) is the unit vector of outer normal on γ at a point ζ and ds is the differential of arc length, then the β-Cauchy-type integral
admits a continuous extension to γ and a version of the Sokhotski–Plemelj formulas holds. Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 11, pp. 1443–1448, November, 2008.  相似文献   

10.
Sharp two-sided estimates are obtained for the eigenvalues\Gl n of the problem
, where a(x), b(x), c(x), and g(x) are bounded measurable functions satisfying the conditions v ⩽ a(x)ξ2 + 2b(x)+η+c(x)η2⩽1,v>0,ξ22=1,|g(x)|⩽δ,δ⩾0. For fixed ν>0 and δ≥0 we have the following exact inequalities:
. In the special case of the problem (0.1) (a(x)≡b(x) and b(x)≡0), sharp two-sided estimates are also proved. Bibliography: 6 titles. Translated fromProblemy Matematicheskogo Analiza, No. 19, 1999, pp. 215–243.  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