共查询到20条相似文献,搜索用时 15 毫秒
1.
LiJunjie BianBaojun 《高校应用数学学报(英文版)》2000,15(3):273-280
The following regularity of weak solutions of a class of elliptic equations of the form are investigated. 相似文献
2.
In this paper we consider special elements of the Fock space #x2131;
n
. That is the space of entire functionsf:ℂ:
n
→ℂ, such that the followingL
2- condition is satisfied:
. Here we show that there exists an entire functiong:ℂ
n
→ℂ such that for every one-dimensional subspace Π⊂ℂ
n
and for all 0<∈<2 we have
, but in the limit case ∈=0 we have
. This result is analogue to a result from [1]. There holomorphic functions on the unit-ball are investigated. Furthermore
the proof — as the one in [1] — uses a theorem from [2]. Therefore we give another application of the results from [2] — namely
for spaces of entire functions. 相似文献
3.
Jacob Korevaar 《Journal d'Analyse Mathématique》2001,85(1):177-194
For entire functionsf whose power series have Hadamard gaps with ratio ≥1+α>1, Gaier has shown that the condition |f(x)|≤e
x forx≥0 implies |f(z)|≤C
αe|z| (*) for allz. Here the result is extended to the case of square root gaps, that is,
, with
, where α>0. Smaller gaps cannot work. In connection with his proof of the general high indices theorem for Borel summability,
Gaier had shown that square root gaps imply
. Having such an estimate, one can adapt Pitt’s Tauberian method for the restricted Borel high indices theorem to show that,
in fact,
, which implies (*). The author also states an equivalent distance formula involving monomialsx
pke−xinL
∞ (0, ∞). 相似文献
4.
周泽华 《中国科学A辑(英文版)》2003,46(1):33-38
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
5.
Let A
0, ... , A
n−1 be operators on a separable complex Hilbert space , and let α0,..., α
n−1 be positive real numbers such that 1. We prove that for every unitarily invariant norm,
for 2 ≤ p < ∞, and the reverse inequality holds for 0 < p ≤ 2. Moreover, we prove that if ω0,..., ω
n−1 are the n roots of unity with ω
j
= e
2πij/n
, 0 ≤ j ≤ n − 1, then for every unitarily invariant norm,
for 2 ≤ p < ∞, and the reverse inequalities hold for 0 < p ≤ 2. These inequalities, which involve n-tuples of operators, lead to natural generalizations and refinements of some of the classical Clarkson inequalities in the
Schatten p-norms. Extensions of these inequalities to certain convex and concave functions, including the power functions, are olso
optained.
相似文献
6.
E. G. Kwon 《Integral Equations and Operator Theory》2009,64(2):251-260
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:
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
(1) | Cf maps Bloch space boundedly into A2p, log α |
(2) | |
(3) | . |
7.
K. J. Wirths 《分析论及其应用》1996,12(3):98-100
Let
be such that |p(eiq)|≤1 for ϕ∈R and |p(1)|=a∈[0,1]. An inequality of Dewan and Govil for the sum |av|+|an|, 0≤u<v≤n is sharpened. 相似文献
8.
全纯函数的加权积分 总被引:1,自引:0,他引:1
Hu Zhangjian Liu Taishun Dept. of Math. Univ. of Sci. Tech. of China Hefei China. Dept. of Math. Huzhou Teachers College Huzhou China. 《高校应用数学学报(英文版)》2004,19(4):474-480
§ 1 IntroductionLet D be the unit disc in the complex plane C,dm be the Lebesgue area measure onD.We denote H (D) the setof all holomorphic functions on D.For 0
相似文献
9.
M. Nowak 《Rendiconti del Circolo Matematico di Palermo》1998,47(3):363-374
In 1986 S. Axler [3] proved that forf∈L
a
2
the Hankel operator
is compact if and only iff is in the little Bloch space {itB}{in0}. In this note we show that the same is true for
, 1<p<∞. Moreover we prove that
is ⋆-compact if and only if
as |z|→1−. 相似文献
10.
E. S. Dubtsov 《Journal of Mathematical Sciences》2007,141(5):1531-1537
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
11.
E. Amar 《Journal of Geometric Analysis》1991,1(4):291-305
We show that if f1, f2 are bounded holomorphic functions in the unit ball
of ℂn such that
, |f1(z)|2 + |f2(z)2|2 ≥ δ2 >; 0, then any functionh in the Hardy space
,p < +∞ can be decomposed ash = f1h1
+ f2h2 with
. The Corona theorem in
would be the same result withp = +∞ and this question is still open forn ≳-2, but the preceding result goes in this direction. 相似文献
12.
Letf(z) be a real entire function of genus 1*, δ≥0, and suppose that for each ε>0, all but a finite number of the zeros off(z) lie in the strip |Imz| ≤δ+ε. Let λ be a positive constant such that
. It is shown that for each ε>0, all but a finite number of the zeros of the entire function
lie in the strip
and if Δ2 < 2λ, then all but a finite number of the zeros of e−λD2
f(z) are real and simple. As a consequence, de Bruijn's question whether the functions eγ
t
2,λ>0, are strong universal factors is answered affirmatively.
The authors wish to acknowledge the financial support of the Korea Research Foundation made in the program year of (1998–2000). 相似文献
13.
In this paper, we show that if the sum ∑r=1∞
Ψ(r) diverges, then the set of points (x, z, w) ∈ ℝ × ℂ × ℚp satisfying the inequalities , and for infinitely many integer polynomials P has full measure. With a special choice of parameters v
i
and λ
i
, i = 1, 2, 3, we can obtain all the theorems in the metric theory of transcendental numbers which were known in the real, complex,
or p-adic fields separately. 相似文献
14.
A. A. Ryabinin 《Mathematical Notes》1998,64(5):629-633
The system
, where Λ={λ
n
} is the set of zeros (of multiplicitiesm
n
) of the Fourier transform
of a singular Cantor-Lebesgue measure, is examined. We prove thate(Λ) is complete and minimal inL
p
(−a, a) withp≥1, and that |L(x+iy)|2 does not satisfy the Muckenhoupt condition on any horizontal line Imz=y≠0 in the complex plane. This implies thate(Λ) does not have the property of convergence extension.
Translated fromMatematicheskie Zametki, Vol. 64, No. 5, pp. 728–733, November, 1998. 相似文献
15.
16.
A. I. Pavlov 《Mathematical Notes》1999,66(4):442-450
The main result of the paper is as follows.Theorem. Suppose that G(z) is an entire function satisfying the following conditions: 1) the Taylor coefficients of the function
G(z) are nonnegative: 2) for some fixed C>0 and A>0 and for |z|>R0, the following inequality holds:
Further, suppose that for some fixed α>0 the deviation DN of the sequence xn={αn}, n=1, 2, ..., as N→∞ has the estimate DN=0(lnB N/N). Then if the function G(z) is not an identical constant and the inequality B+1<A holds, then the power series
converging in the disk |z|<1 cannot be analytically continued to the region |z|>1 across any arc of the circle |z|=1.
Translated fromMatematicheskie Zametki, Vol. 66, No. 4, pp. 540–550, October, 1999. 相似文献
17.
18.
Let
be a polynomial degreen and let
. Then according to Bernstein’s inequality ‖p’‖≤n‖p‖. It is a well known open problem to obtain inequality analogous to Bernstein’s
inequality for the class IIn of polynomials satisfying p(z)≡znp(1/z). Here we obtain an inequality analogous to Bernstein’s inequality for a subclass of IIn. Our results include several of the known results as special cases. 相似文献
19.
20.
Aleksandar Ivić 《Central European Journal of Mathematics》2005,3(2):203-214
Let Δ(x) denote the error term in the Dirichlet divisor problem, and E(T) the error term in the asymptotic formula for the mean square of
. If E
*(t)=E(t)-2πΔ*(t/2π) with
, then we obtain
and
It is also shown how bounds for moments of | E
*(t)| lead to bounds for moments of
. 相似文献