共查询到20条相似文献,搜索用时 15 毫秒
1.
He Ping LIU Xuan Yuan ZHENG 《数学学报(英文版)》2006,22(2):425-430
We consider the commutators of the HSrmander multiplier with CMO-functions on the Heisenberg group. The result of compactness on L^P spaces is proved. 相似文献
2.
Jing Wen LUAN Fu Liu ZHU 《数学学报(英文版)》2005,21(6):1295-1308
In this paper, we make the asymptotic estimates of the heat kernel for the quaternionic Heisenberg group in various cases. We also use these results to deduce the asymptotic estimates of certain harmonic functions on the quaternionic Heisenberg group. Moreover a Martin compactification of the quaternionic Heisenberg group is constructed, and we prove that the Martin boundary of this group is homeomorphic to the unit ball in the quaternionic field. 相似文献
3.
We investigate certain singular integral operators with Riesz-type kernels on s-dimensional Ahlfors-David regular subsets of Heisenberg groups. We show that L
2-boundedness, and even a little less, implies that s must be an integer and the set can be approximated at some arbitrarily small scales by homogeneous subgroups. It follows
that the operators cannot be bounded on many self-similar fractal subsets of Heisenberg groups. 相似文献
4.
We discuss the octonionic regular functions and the octonionic regular operator on the octonionic Heisenberg group. This is the octonionic version of CR function theory in the theory of several complex variables and regular function theory on the quaternionic Heisenberg group. By identifying the octonionic algebra with \(\mathbb{R }^{8}\) , we can write the octonionic regular operator and the associated Laplacian operator as real \((8\times 8)\) -matrix differential operators. Then we use the group Fourier transform on the octonionic Heisenberg group to analyze the associated Laplacian operator and to construct its kernel. This kernel is exactly the Szegö kernel of the orthonormal projection from the space of \(L^{2}\) functions to the space of \(L^{2}\) regular functions on the octonionic Heisenberg group. 相似文献
5.
Ovidiu Calin Der-Chen Chang Haitao Fan 《Journal of Fourier Analysis and Applications》2009,15(6):816-838
There are two parts of this article. We first find explicit formulas for the heat kernel of the sub-elliptic operators $\frac{1}{2}\partial_{x}^{2}-x^{m}\partial_{y}$ with m=0,1,2. We also find the heat kernel for the sub-elliptic operator $\frac{1}{2}\sum_{j=1}^{n}\partial_{x_{j}}^{2}+(\sum_{j=1}^{n}a_{j}x_{j})\partial_{y}$ , with a i constants. In the second part of this paper, we apply results from the first part to construct a close form formula for pricing Asian options on a geometric moving average. 相似文献
6.
TheBergmanKernelFunctionandFullGroupofHolomorphicAutomorphismonaReinhardtDomainGuanBinxin(管冰辛)WangAn(王安)(Dept.ofMath.,Capital... 相似文献
7.
Littlewood Paley g-function on the Heisenberg Group 总被引:2,自引:0,他引:2
He Ping LIU Rui Qin MA 《数学学报(英文版)》2006,22(1):95-100
We consider the g-function related to a class of radial functions which gives a characterization of the L^p-norm of a function on the Heisenberg group. 相似文献
8.
Let f be in the localized nonisotropic Sobolev space
on the n-dimensional
Heisenberg group ℍ
n
= ℂ
n
× ℝ, where 1 = p < Q and Q = 2n + 2 is the homogeneous dimension
of ℍn. Suppose that the subelliptic gradient is gloablly L
p
integrable, i.e.,
is finite.
We prove a Poincaré inequality for f on the entire space ℍ
n
. Using this inequality we prove that the
function f subtracting a certain constant is in the nonisotropic Sobolev space formed by the completion
of
under the norm of
We will also prove that the best constants and extremals for such Poincaré inequalities on ℍ
n
are
the same as those for Sobolev inequalities on ℍ
n
. Using the results of Jerison and Lee on the sharp
constant and extremals for L
2 to
Sobolev inequality on the Heisenberg group, we thus arrive
at the explicit best constant for the aforementioned Poincaré inequality on ℍ
n
when p = 2. We also
derive the lower bound of the best constants for local Poincaré inequalities over metric balls on the
Heisenberg group ℍ
n
.
The first author is supported by Zhongdian grant of NSFC; The second author is supported by a global grant at Wayne State
University and by NSF of USA 相似文献
9.
In this article, we give the derivation algebra Der ? and the automorphism group Aut ? of the twisted Heisenberg–Virasoro algebra ?. 相似文献
10.
We show that the cyclic lamplighter group C 2 ? C n embeds into Hilbert space with distortion $\mathrm{O}(\sqrt{\log n})We show that the cyclic lamplighter group C
2
≀
C
n
embeds into Hilbert space with distortion
O(?{logn})\mathrm{O}(\sqrt{\log n})
. This matches the lower bound proved by Lee et al. (Geom. Funct. Anal., 2009), answering a question posed in that paper. Thus, the Euclidean distortion of C
2
≀
C
n
is
\varTheta(?{logn})\varTheta(\sqrt{\log n})
. Our embedding is constructed explicitly in terms of the irreducible representations of the group. Since the optimal Euclidean
embedding of a finite group can always be chosen to be equivariant, as shown by Aharoni et al. (Isr. J. Math. 52(3):251–265,
1985) and by Gromov (see de Cornulier et. al. in Geom. Funct. Anal., 2009), such representation-theoretic considerations suggest a general tool for obtaining upper and lower bounds on Euclidean embeddings
of finite groups. 相似文献
11.
Bruno Franchi Raul Serapioni Francesco Serra Cassano 《Journal of Geometric Analysis》2011,21(4):1044-1084
We study the notion of intrinsic Lipschitz graphs within Heisenberg groups, focusing our attention on their Hausdorff dimension
and on the almost everywhere existence of (geometrically defined) tangent subgroups. In particular, a Rademacher type theorem
enables us to prove that previous definitions of rectifiable sets in Heisenberg groups are natural ones. 相似文献
12.
SupportingFunctionsandTheDifferentiabilitiesoftheNormsonBanachSpaces¥WangJiangen(王建根)(LuoyangTeacher'sCollege)Abstract:Inthis... 相似文献
13.
Yu Xin DONG Guo Zhen LU Li Jing SUN 《数学学报(英文版)》2007,23(4):35-744
Let f be in the localized nonisotropic Sobolev space Wloc^1,p (H^n) on the n-dimensional Heisenberg group H^n = C^n ×R, where 1≤ p ≤ Q and Q = 2n + 2 is the homogeneous dimension of H^n. Suppose that the subelliptic gradient is gloablly L^p integrable, i.e., fH^n |△H^n f|^p du is finite. We prove a Poincaré inequality for f on the entire space H^n. Using this inequality we prove that the function f subtracting a certain constant is in the nonisotropic Sobolev space formed by the completion of C0^∞(H^n) under the norm of (∫H^n |f| Qp/Q-p)^Q-p/Qp + (∫ H^n |△H^n f|^p)^1/p. We will also prove that the best constants and extremals for such Poincaré inequalities on H^n are the same as those for Sobolev inequalities on H^n. Using the results of Jerison and Lee on the sharp constant and extremals for L^2 to L(2Q/Q-2) Sobolev inequality on the Heisenberg group, we thus arrive at the explicit best constant for the aforementioned Poincaré inequality on H^n when p=2. We also derive the lower bound of the best constants for local Poincaré inequalities over metric balls on the Heisenberg group H^n. 相似文献
14.
Alessandro Veneruso 《Monatshefte für Mathematik》2000,130(3):231-252
Let be the Heisenberg group of dimension . Let be the partial sub-Laplacians on and T the central element of the Lie algebra of . For any we prove that the operator is bounded on the Hardy spaces , if the function m satisfies a Hrmander-type condition on which depends on . We also obtain analogous results for the operators and , where the function m satisfies analogous H?rmander-type conditions on and on , respectively. Here is the Kohn-Laplacian on .
(Received 28 July 1999; in final form 6 March 2000) 相似文献
15.
16.
The Structure of Hypergroup on the Cyclical Group 总被引:2,自引:0,他引:2
TheStructureofHypergroupontheCyclicalGroup¥ZhongYubin(Departmentofmathematics,GuangzhouTeachersCollege)Abstract:Sincethehyper... 相似文献
17.
Based on the concepts of a generalized critical point and the corresponding generalized P.S. condition introduced by Duong Minh Duc [1], we have proved a new Z2 index theorem and get a result on multiplicity of generalized critical points. Using the result and a quite standard variational method, it is found that the equation-ΔHnu = |u|p-1u,x∈Hnhas infinite positive solutions. Our approach can also be applied to study more general nonlinear problems. 相似文献
18.
Hassen Ben Mohamed 《The Ramanujan Journal》2010,21(2):145-171
In this work, we consider the Jacobi-Dunkl operator Λ
α,β
,
a 3 b 3 \frac-12\alpha\geq\beta\geq\frac{-1}{2}
,
a 1 \frac-12\alpha\neq\frac{-1}{2}
, on ℝ. The eigenfunction
Yla,b\Psi_{\lambda}^{\alpha,\beta}
of this operator permits to define the Jacobi-Dunkl transform. The main idea in this paper is to introduce and study the Jacobi-Dunkl
transform and the Jacobi-Dunkl convolution product on new spaces of distributions 相似文献
19.
It is studied systematically for the level strcture of the kernel and hull on continuous-lattice-calued function.In terms of these results,the level characterixations of induced space are odtained. 相似文献
20.
Qi Keng LU 《数学学报(英文版)》2005,21(3):449-456
Since the quaternion ball was used to study the AdS/CFT problems tor spinor fields, it is worthwhile to study further the geometry (in sense of Klein) and analysis on it and on its extended space (in the sense of Behnke-Thullen), the quaternion projective space. 相似文献