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周春琴 《高校应用数学学报(A辑)》2002,17(3):323-328
讨论一类映入球面的满足拟单调不等式的弱调和映射的边界正则性。利用函数的延拓技巧以及Hardy空间和BMO空间的对偶性,对这类弱调和映射的边界正则性给出一个简明的证明。 相似文献
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研究了退化弱(k1,k2)拟正则映射的正则性.利用H lder不等式、Sobolev空间的空间分析方法,以及内插定理等工具,给出了退化弱(k1,k2)拟正则映射事实上为退化(k1,k2)拟正则映射的一个充分条件,其结果对非退化情形也成立. 相似文献
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关于submeso紧空间的映射定理 总被引:4,自引:0,他引:4
证明了在正则空间中闭Lindelof映射保持且逆保持submeso紧性,这改进了林寿关于正则空间完备映射保持且逆保持submeso紧性这一结果;同时我们引用一个反例说明原象空间的正则性是必要的. 相似文献
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研究了退化弱(k1,k2)拟正则映射的正则性.利用Holder不等式、Sobolev空间的空间分析方法,以及内插定理等工具,给出了退化弱(k1,k2)拟正则映射事实上为退化(k1,k2)拟正则映射的一个充分条件,其结果对非退化情形也成立. 相似文献
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对于低于自然可积指数Sobolev类Wloc1,p(Ω,Rn)(1<p<n)的弱拟正则映射,建立了其广义微商可积指数提高到大于空间维数n结果,从而得出拟正则映射的可去奇异集的Hausdorff维数大于零的结论.本文是从弱拟正则映射定义出发对Iwaniec的有关结果给出一个简化证明. 相似文献
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By applying the theory of quasiconformal maps in measure metric spaces that was introduced by Heinonen-Koskela, we characterize
bi-Lipschitz maps by modulus inequalities of rings and maximal, minimal derivatives in Q-regular Loewner spaces. Meanwhile the sufficient and necessary conditions for quasiconformal maps to become bi-Lipschitz
maps are also obtained. These results generalize Rohde’s theorem in ℝ
n
and improve Balogh’s corresponding results in Carnot groups.
This research is supported by China NSF (Grant No. 10271077) 相似文献
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In the paper [Monotone countable paracompactness and maps to ordered topological vector spaces, Top. Appl., 2014, 169(3): 51–70], Yamazaki initiated the study on maps with values into ordered topological vector spaces. Characterizations of monotonically countably paracompact spaces and some other spaces in terms of maps to ordered topological vector spaces were obtained. In this paper, following Yamazaki's method, we present some characterizations of stratifiable spaces and k-semi-stratifiable spaces in terms of maps with values into ordered topological vector spaces. 相似文献
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本文研究有序拓扑向量空间中非线性映照的共鸣定理.对于取值于有序拓扑向量空间中的映照,利用序关系,引入了一类广泛的非线性映照.对于这类非线性映照,应用纲理论,并给出了关于点态序有界蕴涵一致序有界的共鸣定理. 相似文献
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Juha Heinonen Pekka Koskela Nageswari Shanmugalingam Jeremy T. Tyson 《Journal d'Analyse Mathématique》2001,85(1):87-139
We give a definition for the class of Sobolev functions from a metric measure space into a Banach space. We give various characterizations
of Sobolev classes and study the absolute continuity in measure of Sobolev mappings in the “borderline case”. We show under
rather weak assumptions on the source space that quasisymmetric homeomorphisms belong to a Sobolev space of borderline degree;
in particular, they are absolutely continuous. This leads to an analytic characterization of quasiconformal mappings between
Ahlfors regular Loewner spaces akin to the classical Euclidean situation. As a consequence, we deduce that quasisymmetric
maps respect the Cheeger differentials of Lipschitz functions on metric measure spaces with borderline Poincaré inequality.
J. H. supported by NSF grant DMS9970427. P. K. supported by the Academy of Finland, project 39788. N. S. supported in part
by Enterprise Ireland. J. T. T. supported by an NSF Postdoctoral Research Fellowship. 相似文献
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本文研究了欧式空间上拟对称映射的不变量问题,利用定义集合间隔序列的方法,获得了一个新的d-维拟对称映射的不变量,深化了Lipschitz不变量研究中类似的结果. 相似文献
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本文主要考虑度量空间中拟双曲一致域与拟对称映射之间的关系,并证明了度量空间中拟双曲一致域在拟对称映射下仍然是保持不变的. 相似文献
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Alireza Ranjbar-Motlagh 《Journal of Mathematical Analysis and Applications》2022,505(2):125508
The purpose of this article is to study the Besov type function spaces for maps which are defined on abstract metric-measure spaces. We extend some of the embedding theorems of the classical Besov spaces to the setting of abstract spaces. 相似文献
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In this work, using lacunary sequences and the notion of ideal convergence we define and examine new sequence spaces with respect to a sequence of modulus functions in n-normed linear spaces. Further, the definition of Iθ-convergence in n-normed linear spaces and some related results are given. 相似文献
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Dragomir Saric 《Proceedings of the American Mathematical Society》2008,136(3):889-897
We give a short proof of the fact that bounded earthquakes of the unit disk induce quasisymmetric maps of the unit circle. By a similar method, we show that symmetric maps are induced by bounded earthquakes with asymptotically trivial measures.
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本文在Bergman空间Bqp(01)中研究关于旋转连续模的Hardy Littlewood逆定理,在通常条件下,得到了与在空间Hp(0
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