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1.
The main theorem of this article is a characterization of non compact simply connected complete Kobayashi hyperbolic complex
manifold of dimension n≽ 2 with real n
2-dimensional holomorphic automorphism group. Together with the earlier work [11, 12] and [13] of Isaev and Krantz, this yields
a complete classification of the simply-connected, complete Kobayashi hyperbolic manifolds with dimℝ Aut (M) ≽ (dimℂ
M)2. 相似文献
2.
PengYanHU WenJunZHANG 《数学学报(英文版)》2004,20(2):261-272
In this paper the small Hankel operators on the Dirichlet-type spaces Dp on the unit ball of C^n are considered. A similar result to that of the one-dimensional setting is given, which characterizes the boundedness of the small Hankel operators on Dp. 相似文献
3.
In this paper, we get W
1,p
(R
n
)-boundedness for tangential maximal function and nontangential maximal function, which improves J.Kinnunen, P.Lindqvist and
Tananka’s results.
Supported by the key Academic Discipline of Zhejiang Province of China under Grant No.2005 and the Zhejiang Provincial Natural
Science Foundation of China. 相似文献
4.
We consider the mixed problem,
in a class of Lipschitz graph domains in two dimensions with Lipschitz constant at most 1. We suppose the Dirichlet data,
f
D
, has one derivative in L
p
(D) of the boundary and the Neumann data, f
N
, is in L
p
(N). We find a p
0 > 1 so that for p in an interval (1, p
0), we may find a unique solution to the mixed problem and the gradient of the solution lies in L
p
.
L. Lanzani, L. Capogna and R. M. Brown were supported, in part, by the U.S. National Science Foundation. 相似文献
5.
H. Beirão da Veiga 《Mathematische Annalen》2005,331(1):203-217
We give a simple and very complete proof of the existence of a strong (H2) solution to the non-homogeneous problem (1.1) under the non homogeneous boundary conditions (1.6). Here we consider the half-space case = Rn+, n 3, see theorem 1.2. This regularity result was previously obtained by Solonnikov and adilov in reference [33] for the classical Stokes system (==0, g(x)=0) in the 3–D homogenous case (a=0, b=0) and a suitable open subset of R3.Partly supported by CMAF/UL and FCT. 相似文献
6.
We show that if the group of holomorphic automorphisms of a connected complex manifold M of dimension n is isomorphic as a
topological group equipped with the compact-open topology to the automorphism group of the unit ball B
n ⊂ ℂ
n
,then M is biholomorphically equivalent to B
n. 相似文献
7.
LiangYuLIN ChunHuiQIU 《数学学报(英文版)》2004,20(6):989-998
Suppose that D is a bounded domain with a piecewise C^1 smooth boundary in C^n. Let ψ∈C^1 α(δD). By using the Hadamard principal value of the higher order singular integral and solid angle coefficient method of points on the boundary, we give the Plemelj formula of the higher order singular integral with the Boehner-Martinelli kernel, which has integral density ψ. Moreover, by means of the Plemelj formula and methods of complex partial differential equations, we discuss the corresponding Cauehy boundary value problem with the Boehner-Martinelli kernel on a closed piecewise smooth manifold and obtain its unique branch complex harmonic solution. 相似文献
8.
Ian Wood 《Mathematische Zeitschrift》2007,255(4):855-875
We consider the Laplacian with Dirichlet or Neumann boundary conditions on bounded Lipschitz domains Ω, both with the following
two domains of definition: , or , where B is the boundary operator. We prove that, under certain restrictions on the range of p, these operators generate positive analytic contraction semigroups on L
p
(Ω) which implies maximal regularity for the corresponding Cauchy problems. In particular, if Ω is bounded and convex and
, the Laplacian with domain D
2(Δ) has the maximal regularity property, as in the case of smooth domains. In the last part, we construct an example that
proves that, in general, the Dirichlet–Laplacian with domain D
1(Δ) is not even a closed operator.
The main results of this paper are taken from the author’s Ph.D. thesis, written at the TU Darmstadt under the supervision
of Prof. M. Hieber. The author wishes to thank Prof. Hieber for his guidance, encouragement and support in the last few years.
Many thanks also go to Prof. C. E. Kenig for his hospitality and many ruitful discussions on the subject during a 1-year stay
at the University of Chicago. 相似文献
9.
Bao Qin Li 《Mathematische Zeitschrift》2008,258(4):763-771
We show that meromorphic solutions f, g of f
2 + g
2 = 1 in C2 must be constant, if f
z2 and g
z1 have the same zeros (counting multiplicities). We also apply the result to characterize meromorphic solutions of certain
nonlinear partial differential equations. 相似文献
10.
We classify graph C
*-algebras, namely, Cuntz-Krieger algebras associated to the Bass-Hashimoto edge incidence operator of a finite graph, up to
strict isomorphism. This is done by a purely graph theoretical calculation of the K-theory of the C
*-algebras and the method also provides an independent proof of the classification up to Morita equivalence and stable equivalence
of such algebras, without using the boundary operator algebra. A direct relation is given between the K
1-group of the algebra and the cycle space of the graph.
We thank Jakub Byszewski for his input in Sect. 2.8. The position of the unit in K
0(
Ч) was guessed based on some example calculations by Jannis Visser in his SCI 291 Science Laboratory at Utrecht University
College. 相似文献
11.
Rasul Shafikov 《Inventiones Mathematicae》2003,152(3):665-682
The following result is proved: Let D and D′ be bounded domains in ℂ
n
, ∂D is smooth, real-analytic, simply connected, and ∂D′ is connected, smooth, real-algebraic. Then there exists a proper holomorphic correspondence f:D→D′ if and only if there exist points p∈∂D and p′∈∂D′, such that ∂D and ∂D′ are locally CR-equivalent near p and p′. This leads to a characterization of the equivalence relationship between bounded domains in ℂ
n
modulo proper holomorphic correspondences in terms of local CR-equivalence of their boundaries.
Oblatum 23-I-2002 & 18-XI-2002?Published online: 17 February 2003 相似文献
12.
Milutin Dostanić 《Journal d'Analyse Mathématique》2008,104(1):13-23
It is shown that the Berezin transform B on L
p
(D), where D is the unit disc, has norm
. Furthermore, the norms of a family of operators (on L
p
(D)) whose kernels are moduli of Bergman type kernels are also calculated.
Partially supported by MNZZS, Grant
ON144010 相似文献
13.
Zhang Pu Wu Huoxiong 《高校应用数学学报(英文版)》2005,20(4):455-461
Let μΩ,b be the commutator generalized by the n-dimensional Marcinkiewicz integral μΩ and a function b∈ BMO(R^n). It is proved that μΩ,bis bounded from the Hardy space H^1 (R^n) into the weak L^1(R^n) space. 相似文献
14.
Joseph Corneli Neil Hoffman Paul Holt George Lee Nicholas Leger Stephen Moseley Eric Schoenfeld 《Journal of Geometric Analysis》2007,17(2):189-212
We prove the double bubble conjecture in the three-sphereS
3 and hyperbolic three-spaceH
3 in the cases where we can apply Hutchings theory:
A balancing argument and asymptotic analysis reduce the problem inS
3 andH
3 to some computer checking. The computer analysis has been designed and fully implemented for both spaces. 相似文献
– | • InS 3, when each enclosed volume and the complement occupy at least 10% of the volume ofS 3. |
– | • inH 3, when the smaller volume is at least 85% that of the larger. |
15.
The following result is proved: Let be a n-dimensional C1-submanifold of RN which is domain of a given nRN-valued map of class C1. Then the set of all points P such that (P) is non-zero, simple and enveloped by TP is C2-rectifiable. As a corollary we get a criterion for the C2-rectifiability of a rectifiable set based on the rectifiability of some generalized Gauss lift to the Grassmanian bundle RN×G(N,n). Mathematics Subject Classification (2000) Primary 49Q15, 53A07; Secondary 49Q20, 49N60 相似文献
16.
In this article we study the problem of extending Fourier
Multipliers on L
p
(T) to those on L
p
(R)
by taking convolution with a kernel, called a summability
kernel. We characterize the space of such kernels
for the cases p = 1 and p = 2. For other values of p we give a
necessary condition for a function to be a
summability kernel. For the case p = 1, we present
properties of measures which are transferred from M(T) to
M(R) by summability kernels. Furthermore it is
shown that every l
p
sequence can be extended to some
L
q
(R) multipliers for certain values of p and q. 相似文献
17.
Sh. A. Ayupov 《Functional Analysis and Its Applications》2004,38(4):302-304
Let R be a real AW
*-algebra, and suppose that its complexification M = R + iR is also a (complex) AW
*-algebra. We prove that R is of type I if and only if so is M.Translated from Funktsionalnyi Analiz i Ego Prilozheniya, Vol. 38, No. 4, pp. 79–81, 2004Original Russian Text Copyright © by Sh. A. Ayupov 相似文献
18.
Piotr Kalemba Szymon Plewik Anna Wojciechowska 《Central European Journal of Mathematics》2008,6(2):218-227
The σ-ideal (v
0) is associated with the Silver forcing, see [5]. Also, it constitutes the family of all completely doughnut null sets, see
[9]. We introduce segment topologies to state some resemblances of (v
0) to the family of Ramsey null sets. To describe add(v
0) we adopt a proof of Base Matrix Lemma. Consistent results are stated, too. Halbeisen’s conjecture cov(v
0) = add(v
0) is confirmed under the hypothesis t = min{cf(c), r}. The hypothesis cov(v
0) = ω
1 implies that (v
0) has the ideal type (c, ω
1, c).
相似文献
19.
In this paper, we give a definition of Bloch mappings defined in the unit polydisk D
n
, which generalizes the concept of Bloch functions defined in the unit disk D. It is known that Bloch theorem fails unless we have some restrictive assumption on holomorphic mappings in several complex
variables. We shall establish the corresponding distortion theorems for subfamilies β(K) and β
loc(K) of Bloch mappings defined in the polydisk D
n
, which extend the distortion theorems of Liu and Minda to higher dimensions. As an application, we obtain lower and upper
bounds of Bloch constants for various subfamilies of Bloch mappings defined in D
n
. In particular, our results reduce to the classical results of Ahlfors and Landau when n = 1.
This work was supported by the National Natural Science Foundation of China (Grant No. 10571164) and Specialized Research
Fund for the Doctoral Program of Higher Education (SRFDP) (Grant No. 20050358052) 相似文献
20.
Jaigyoung Choe Mohammad Ghomi Manuel Ritoré 《Calculus of Variations and Partial Differential Equations》2007,29(4):421-429
We prove that the area of a hypersurface Σ which traps a given volume outside a convex domain C in Euclidean space R
n
is bigger than or equal to the area of a hemisphere which traps the same volume on one side of a hyperplane. Further, when
C has smooth boundary ∂C, we show that equality holds if and only if Σ is a hemisphere which meets ∂C orthogonally. 相似文献