共查询到20条相似文献,搜索用时 312 毫秒
1.
In this note, we prove the boundary unique continuation property for harmonic function dfined on convex domain 相似文献
2.
主要研究调和函数和Poisson方程的解的性质.讨论了调和函数的Lipschitz型空间,建立了调和函数的Schwarz-Pick型引理,并利用所得结果证明了与调和Hardy空间有关的一个Landau-Bloch型定理.最后,还利用正规族理论讨论了与Poisson方程的解有关的Landau-Bloch型定理的存在性. 相似文献
3.
Hardy空间中的Bloch函数 总被引:1,自引:0,他引:1
本文利用单位圆盘内解析函数的Shimizu-Ahlfors特征函数分给出了Hardy空间中Bloch函数和BMOA的新特征。由此我们发现了B∩Hp(0<p<∞)与BMOA之间的本质差别。 相似文献
4.
Jiaxi Jiu & Zhongkai Li 《分析论及其应用》2020,36(3):326-347
We consider the local boundary values of generalized harmonic functions associated with the rank-one Dunkl operator $D$ in the upper half-plane $R^{2}_+=R\times(0,\infty)$, where $$(Df)(x)=f'(x)+(\lambda/x)[f(x)-f(-x)]$$ for given $\lambda\ge0$. A $C^2$ function $u$ in $R^{2}_+$ is said to be $\lambda$-harmonic if $(D_x^2+\partial_{y}^2)u=0$. For a $\lambda$-harmonic function $u$ in $R^{2}_+$ and for a subset $E$ of $\partial R^{2}_+=R$ symmetric about $y$-axis, we prove that the following three assertions are equivalent: (i) $u$ has a finite non-tangential limit at $(x,0)$ for a.e. $x\in E$; (ii) $u$ is non-tangentially bounded for a.e. $x\in E$; (iii) $(Su)(x)<\infty$ for a.e. $x\in E$, where $S$ is a Lusin-type area integral associated with the Dunkl operator $D$. 相似文献
5.
Potential Analysis - Assume that a bounded domain Ω??N (N ≥ 2) has the property that there exists a signed measure µ with compact support in Ω such that, for every... 相似文献
6.
设(X,d,μ)是满足非负Ricci曲率条件的度量测度空间.本文研究了(开)上半空间X×R+上调和函数的边界问题.我们得到了:若u(x,t)是定义在上半空间X×R+上的调和函数,且满足Carleson测度条件supxB,rB∫rB0fB(xB,rB)|t▽u(x,t)|2dμ(x)dt/t≤C<∞,其中▽=(▽x,?)... 相似文献
7.
8.
K. -J. Wirths 《Constructive Approximation》1999,15(3):427-440
In this paper we construct Bloch functions F for which the set {z | e sup
|ζ| < 1
|F'(ζ)| ( 1 - |ζ|
2
) = |F'(z)| ( 1 - |z|
2
)} is an analytic Jordan curve tangential to the unit disk in some points. It is proved that, using such functions, we can
derive analogs to the Taylor expansion for Bloch functions in cases where the Taylor expansion does not converge.
October 15, 1997. Date revised: March 12, 1998. Date accepted: June 18, 1998. 相似文献
9.
Bloch型函数的高阶径向导数 总被引:1,自引:0,他引:1
讨论了复超球上全纯函数的高阶导数的增长速度 ,证明了f∈Bα 的充分必要条件是supa∈B(1- |z|2 ) m+α- 1|Rmf(z) | <∞ ,或supa∈B∫B(1-|z|2 ) (m+α- 1) |Rmf(z) |pJRφα(z)dv(z) <∞ ,或 (1- |z|2 ) p(m+α- 1) |Rmf(z) |pdv(z)是Bergman Carleson测度 . 相似文献
10.
Zhongwei Shen 《数学学报(英文版)》2019,35(6):1074-1084
Let L be a second-order linear elliptic operator with complex coefficients. It is shown that if the Lp Dirichlet problem for the elliptic system L(u) = 0 in a fixed Lipschitz domain Ω in... 相似文献
11.
Xavier Tolsa 《纯数学与应用数学通讯》2023,76(2):305-336
Let be a domain, or more generally, a Lipschitz domain with small local Lipschitz constant. In this paper it is shown that if u is a function harmonic in and continuous in , which vanishes in a relatively open subset ; moreover, the normal derivative vanishes in a subset of with positive surface measure; then u is identically zero. © 2021 The Authors. Communications on Pure and Applied Mathematics published by Wiley Periodicals LLC. 相似文献
12.
Under the assumption that the underlying measure is a non-negative Radon measure which only satisfies some growth condition, the authors prove that for a class of commutators with Lipschitz functions which include commutators generated by Calderon-Zygmund operators and Lipschitz functions as examples, their boundedness in Lebesgue spaces or the Hardy space H1 (μ) is equivalent to some endpoint estimates satisfied by them. This result is new even when the underlying measureμis the d-dimensional Lebesgue measure. 相似文献
13.
《偏微分方程通讯》2013,38(1-2):91-109
Abstract Let Ω be a bounded Lipschitz domain in ? n , n ≥ 3 with connected boundary. We study the Robin boundary condition ?u/?N + bu = f ∈ L p (?Ω) on ?Ω for Laplace's equation Δu = 0 in Ω, where b is a non-negative function on ?Ω. For 1 < p < 2 + ?, under suitable compatibility conditions on b, we obtain existence and uniqueness results with non-tangential maximal function estimate ‖(?u)*‖ p ≤ C‖f‖ p , as well as a pointwise estimate for the associated Robin function. Moreover, the solution u is represented by a single layer potential. 相似文献
14.
The existence and uniqueness theorem for isotropic hypersurfaces with prescribed boundary in Lorentzian warped products is
proved.The proof is based on minimal Lipschitz extensions of functions.
__________
Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 39, No. 3, pp. 28–36, 2005
Original Russian Text Copyright #x00A9; by A. A. Klyachin and V. M. Miklyukov 相似文献
15.
Robert F. Allen 《分析论及其应用》2014,(2):236-248
We study the bounded and the compact weighted composition operators from the Bloch space into the weighted Banach spaces of holomorphic functions on bounded homogeneous domains, with particular attention to the unit polydisk. For bounded homogeneous domains, we characterize the bounded weighted composition operators and determine the operator norm. In addition, we provide sufficient conditions for compactness. For the unit polydisk, we completely characterize the compact weighted composition operators, as well as provide "computable" estimates on the operator norm. 相似文献
16.
The boundedness of commutators of multilinear singular integrals with Lipschitz functions in product Lebesgue spaces is obtained. 相似文献
17.
We study the behaviour of harmonic functions on a homogeneous tree from the point of view of the tangential boundary covergence. 相似文献
18.
Suppose that
is an arbitrary finite complex Borel measure on the interval
is its Poisson integral,
and
are the conjugate harmonics of
, and
is the nontangential limiting value of the analytic function
as
. In this paper, we consider the problem of representing the analytic function
in terms of its boundary values
. 相似文献
19.
In this paper, we prove two-sided pointwise estimates for the Green function of a parabolic operator with singular first order term on a C1,1-cylindrical domain . Basing on these estimates, we establish the equivalence of the parabolic measure, the adjoint parabolic measure and the surface measure on the lateral boundary of . These results are first studied by some authors for certain elliptic and less general parabolic operators.
Mathematics Subject Classifications (2000) 31B25, 35B05, 35K10, 58J35. 相似文献
20.