共查询到20条相似文献,搜索用时 0 毫秒
1.
Miroslav Engliš 《复变函数与椭圆型方程》2015,60(12):1712-1726
We obtain a formula for the Sobolev inner product in standard weighted Bergman spaces of holomorphic functions on a bounded symmetric domain in terms of the Peter–Weyl components in the Hua–Schmidt decomposition, and use it to clarify the relationship between the analytic continuation of these standard weighted Bergman spaces and the Sobolev spaces on bounded symmetric domains. 相似文献
2.
The classical Sobolev embedding theorem of the space of functions of bounded variation BV(Rn) into Ln′(Rn) is proved in a sharp quantitative form. 相似文献
3.
Ralph Howard 《Proceedings of the American Mathematical Society》1998,126(9):2779-2787
Let be a complete two dimensional simply connected Riemannian manifold with Gaussian curvature . If is a compactly supported function of bounded variation on , then satisfies the Sobolev inequality
Conversely, letting be the characteristic function of a domain recovers the sharp form of the isoperimetric inequality for simply connected surfaces with . Therefore this is the Sobolev inequality ``equivalent' to the isoperimetric inequality for this class of surfaces. This is a special case of a result that gives the equivalence of more general isoperimetric inequalities and Sobolev inequalities on surfaces.
Under the same assumptions on , if is a closed curve and is the winding number of about , then the Sobolev inequality implies
which is an extension of the Banchoff-Pohl inequality to simply connected surfaces with curvature .
4.
Hong-liang Li 《高校应用数学学报(英文版)》2012,27(3):371-378
Let X be a rearrangement invariant space in R n and $W_X^{r_1 ,...,r_n } $ be an anisotropic Sobolev space which is a generalization of $W_p^{r_1 ,...,r_n } $ . The main subject of this paper is to prove the embedding theorem for $W_X^{r_1 ,...,r_n } $ . 相似文献
5.
Interpolation theorems on weighted Lorentz martingale spaces 总被引:2,自引:0,他引:2
Yong JIAO~ Li-ping FAN Pei-de LIU School of Mathematics Statistics Wuhan University Wuhan China 《中国科学A辑(英文版)》2007,50(9):1217-1226
In this paper several interpolation theorems on martingale Lorentz spaces are given.The proofs are based on the atomic decompositions of martingale Hardy spaces over weighted measure spaces.Applying the interpolation theorems,we obtain some inequalities on martingale transform operator. 相似文献
6.
K. Watanabe Y. Kametaka K. Takemura 《Journal of Mathematical Analysis and Applications》2008,340(1):699-706
The best constants Cm,j of Sobolev embedding of Hm(0,a) into Cj[0,a](0?j?m−1) are obtained. Especially, when a=∞, these constants can be represented in a closed form. 相似文献
7.
Qianqiao Guo 《Journal of Differential Equations》2019,266(12):8258-8280
Consider the integral equation where is a smooth bounded domain. For , the existence of energy maximizing positive solution in the subcritical case , and nonexistence of energy maximizing positive solution in the critical case are proved in [6]. For , the existence of energy minimizing positive solution in the subcritical case , and nonexistence of energy minimizing positive solution in the critical case are also proved in [4]. Based on these, in this paper, the blowup behaviour of energy maximizing positive solution as (in the case of ), and the blowup behaviour of energy minimizing positive solution as (in the case of ) are analyzed. We see that for the blowup behaviour obtained is quite similar to that of the elliptic equation involving the subcritical Sobolev exponent. But for , different phenomena appear. 相似文献
8.
Zhonghai Ding 《Proceedings of the American Mathematical Society》1996,124(2):591-600
A complete proof of the trace theorem of Sobolev spaces on Lipschitz domains has not appeared in the literature yet. The purpose of this paper is to give a complete proof of the trace theorem of Sobolev spaces on Lipschitz domains by taking advantage of the intrinsic norm on . It is proved that the trace operator is a linear bounded operator from to for .
9.
We characterize the real interpolation space between a weighted space and a weighted Sobolev space in arbitrary bounded domains in , with weights that are positive powers of the distance to the boundary. 相似文献
10.
We prove Harnack's inequality for first eigenfunctions of the p-Laplacian in metric measure spaces. The proof is based on the famous Moser iteration method, which has the advantage that it only requires a weak (1,p)-Poincaré inequality. As a by-product we obtain the continuity and the fact that first eigenfunctions do not change signs in bounded domains. 相似文献
11.
We give a definition of Bloch space on bounded symmetric domains in arbitrary complex Banach space and prove such function
space is a Banach space. The properties such as boundedness, compactness and closed range of composition operators on such
Bloch space are studied.
Dedicated to Professor Sheng GONG on the occasion of his 75th birthday 相似文献
12.
Yoshihiro Mizuta Tetsu Shimomura 《Proceedings of the American Mathematical Society》2002,130(10):2985-2994
Our aim in this paper is to discuss continuity and differentiability of functions in weighted Sobolev spaces in the limiting case of Sobolev's imbedding theorem.
13.
Sanja Maruši? 《Journal of Mathematical Analysis and Applications》2002,272(2):575-581
In this paper we study the asymptotic behaviour of the constants in Sobolev inequalities in thin domains with respect to the thickness of the domain ε. We prove that the sharp Sobolev constants in thin domains converge to the sharp Sobolev constant on the lower-dimensional domain, as ε tends to zero. 相似文献
14.
In this article, by extending classical Dellacherie's theorem on stochastic sequences to variable exponent spaces, we prove that the famous Burkholder-Gundy-Davis inequality holds for martingales in variable exponent Hardy spaces. We also obtain the variable exponent analogues of several martingale inequalities in classical theory, including convexity lemma, Chevalier's inequality and the equivalence of two kinds of martingale spaces with predictable control. Moreover, under the regular condition on σ-algebra sequence we prove the equivalence between five kinds of variable exponent martingale Hardy spaces. 相似文献
15.
杨大春 《中国科学A辑(英文版)》2003,46(5)
This paper introduces the fractional Sobolev spaces on spaces of homogeneous type,includingmetric spaces and fractals. These Sobolev spaces include the well-known Hajfasz-Sobolev spaces as specialmodels.The author establishes varions chaaracterizations of(sharp)maximal functions for these spaces.Asapplications,the author identifies the fractional Sobolev spaces with some Lipscitz-type spaces.Moreover;some embedding theorems are also given. 相似文献
16.
Janusz Matkowski 《Journal of Mathematical Analysis and Applications》2008,348(1):315-323
Let (Ω,Σ,μ) a measure space such that 0<μ(A)<1<μ(B)<∞ for some A,B∈Σ. Under some natural conditions on the bijective functions φ,φ1,φ2,ψ,ψ1,ψ2:(0,∞)→(0,∞) we prove that if
17.
Sergey A. Nazarov Andrey S. Slutskij Jari Taskinen 《Mathematical Methods in the Applied Sciences》2014,37(16):2463-2483
We consider an elastic rod with rounded ends and diameter proportional to a small parameter h > 0. The roundness of the ends is described by an exponent m ∈ (0,1). We derive for the rod an asymptotically sharp Korn inequality with a special weighted anisotropic norm. Weight factors with m‐dependent powers of h appear both in the anisotropic norm and the Korn inequality itself, and we discover three critical values m = 1 ∕ 4, m = 1 ∕ 2 and m = 3 ∕ 4 at which these exponents are crucially changed. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
18.
Tengiz Kopaliani George Chelidze 《Journal of Mathematical Analysis and Applications》2009,356(1):232-817
We prove analogies of the classical Gagliardo-Nirenberg inequalities
19.
Thorsten Thies 《manuscripta mathematica》2003,111(1):97-104
We prove an isoperimetric inequality for compact, regular domains in rank one symmetric spaces, which is sharp for geodesic
balls. Besides volume and area of a given domain, some weak information about the second fundamental form of its boundary
is involved.
Received: 2 September 2002 / Revised version: 10 December 2002
Published online: 20 March 2003
Mathematics Subject Classification (2000): 53C35, 52A40, 51M25 相似文献
20.
A class of pseudo-monotone operators and its applications in PDE 总被引:3,自引:0,他引:3
In this paper we give a criterion of pseudo-monotone operators by which a class of operators related to elliptic partial differential
equations is recognized as pseudo-monotone operators. Some applications in boundary value problems for elliptic equations
and obstacle problems are given.
Research supported by the Fund of IMAS 相似文献