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Borderline Case of Traces and Extensions for Weighted Sobolev Spaces 加权Sobolev空间的迹与扩展的边界情况
IF 0.7 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2023-09-15 DOI: 10.1007/s10114-023-1309-5
Man Zi Huang, Xian Tao Wang, Zhuang Wang, Zhi Hao Xu
{"title":"Borderline Case of Traces and Extensions for Weighted Sobolev Spaces","authors":"Man Zi Huang,&nbsp;Xian Tao Wang,&nbsp;Zhuang Wang,&nbsp;Zhi Hao Xu","doi":"10.1007/s10114-023-1309-5","DOIUrl":"10.1007/s10114-023-1309-5","url":null,"abstract":"<div><p>In this paper, we study the traces and the extensions for weighted Sobolev spaces on upper half spaces when the weights reach to the borderline cases. We first give a full characterization of the existence of trace spaces for these weighted Sobolev spaces, and then study the trace parts and the extension parts between the weighted Sobolev spaces and a new kind of Besov-type spaces (on hyperplanes) which are defined by using integral averages over selected layers of dyadic cubes.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50031260","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
The Sufficient and Necessary Conditions of the Strong Law of Large Numbers under Sub-linear Expectations 亚线性预期下强大数定律的充分和必要条件
IF 0.7 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2023-09-15 DOI: 10.1007/s10114-023-1103-4
Li Xin Zhang
{"title":"The Sufficient and Necessary Conditions of the Strong Law of Large Numbers under Sub-linear Expectations","authors":"Li Xin Zhang","doi":"10.1007/s10114-023-1103-4","DOIUrl":"10.1007/s10114-023-1103-4","url":null,"abstract":"<div><p>In this paper, by establishing a Borel–Cantelli lemma for a capacity which is not necessarily continuous, and a link between a sequence of independent random variables under the sub-linear expectation and a sequence of independent random variables on ℝ<sup>∞</sup> under a probability, we give the sufficient and necessary conditions of the strong law of large numbers for independent and identically distributed random variables under the sub-linear expectation, and the sufficient and necessary conditions for the convergence of an infinite series of independent random variables, without the assumption on the continuity of the capacities. A purely probabilistic proof of a weak law of large numbers is also given.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135353863","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
A Semiparametric Additive-multiplicative Rates Model for the Weighted Composite Endpoint of Recurrent and Terminal Events 重复事件和终止事件加权复合端点的半参数加乘率模型
3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2023-09-15 DOI: 10.1007/s10114-023-1170-6
Yi Deng, Qiang Xiong, Shu Wei Li
{"title":"A Semiparametric Additive-multiplicative Rates Model for the Weighted Composite Endpoint of Recurrent and Terminal Events","authors":"Yi Deng, Qiang Xiong, Shu Wei Li","doi":"10.1007/s10114-023-1170-6","DOIUrl":"https://doi.org/10.1007/s10114-023-1170-6","url":null,"abstract":"","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135438300","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Index Estimates for Free Boundary f-minimal Hypersurfaces 自由边界f-极小超曲面的指数估计
IF 0.7 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2023-09-15 DOI: 10.1007/s10114-023-2155-1
Niang Chen, Jian Quan Ge, Miao Miao Zhang
{"title":"Index Estimates for Free Boundary f-minimal Hypersurfaces","authors":"Niang Chen,&nbsp;Jian Quan Ge,&nbsp;Miao Miao Zhang","doi":"10.1007/s10114-023-2155-1","DOIUrl":"10.1007/s10114-023-2155-1","url":null,"abstract":"<div><p>We prove that the index is bounded from below by a linear function of its first Betti number for any compact free boundary <i>f</i>-minimal hypersurface in certain positively curved weighted manifolds.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50031255","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Hazard Model with Random Treatment Time-Lag Effect 具有随机处理时滞效应的危害模型
IF 0.7 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2023-09-15 DOI: 10.1007/s10114-023-1391-8
Xin Ye, Yan Yan Liu
{"title":"Hazard Model with Random Treatment Time-Lag Effect","authors":"Xin Ye,&nbsp;Yan Yan Liu","doi":"10.1007/s10114-023-1391-8","DOIUrl":"10.1007/s10114-023-1391-8","url":null,"abstract":"<div><p>In clinical studies, it is often that the medical treatments take a period of time before having an effect on patients and the delayed time may vary from person to person. Even though there exists a rich literature developing methods to estimate the time-lag period and treatment effects after lag time, most of these existing studies assume a fixed lag time. In this paper, we propose a hazard model incorporating a random treatment time-lag effect to describe the heterogeneous treatment effect among subjects. The EM algorithm is used to obtain the maximum likelihood estimator. We give the asymptotic properties of the proposed estimator and evaluate its performance via simulation studies. An application of the proposed method to real data is provided.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50031256","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
n-exact Categories Arising from n-exangulated Categories 由n个膨胀类别产生的n个精确类别
IF 0.7 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2023-09-15 DOI: 10.1007/s10114-023-1558-3
Jian He, Pan Yue Zhou
{"title":"n-exact Categories Arising from n-exangulated Categories","authors":"Jian He,&nbsp;Pan Yue Zhou","doi":"10.1007/s10114-023-1558-3","DOIUrl":"10.1007/s10114-023-1558-3","url":null,"abstract":"<div><p>Let <span>({cal C})</span> be a Krull–Schmidt <i>n</i>-exangulated category and <span>({cal A})</span> be an <i>n</i>-extension closed subcategory of <span>({cal C})</span>. Then <span>({cal A})</span> inherits the <i>n</i>-exangulated structure from the given <i>n</i>-exangulated category in a natural way. This construction gives <i>n</i>-exangulated categories which are neither <i>n</i>-exact categories in the sense of Jasso nor (<i>n</i> + 2)-angulated categories in the sense of Geiss–Keller–Oppermann in general. Furthermore, we also give a sufficient condition on when an <i>n</i>-exangulated category <span>({cal A})</span> is an <i>n</i>-exact category. These results generalize work by Klapproth and Zhou.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50031257","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 7
A Universal Inequality for Stability of Coarse Lipschitz Embeddings 粗糙Lipschitz嵌入稳定性的一个普遍不等式
IF 0.7 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2023-09-15 DOI: 10.1007/s10114-023-2136-4
Duan Xu Dai, Ji Chao Zhang, Quan Qing Fang, Long Fa Sun, Ben Tuo Zheng
{"title":"A Universal Inequality for Stability of Coarse Lipschitz Embeddings","authors":"Duan Xu Dai,&nbsp;Ji Chao Zhang,&nbsp;Quan Qing Fang,&nbsp;Long Fa Sun,&nbsp;Ben Tuo Zheng","doi":"10.1007/s10114-023-2136-4","DOIUrl":"10.1007/s10114-023-2136-4","url":null,"abstract":"<div><p>Let <i>X</i> and <i>Y</i> be two pointed metric spaces. In this article, we give a generalization of the Cheng–Dong–Zhang theorem for coarse Lipschitz embeddings as follows: If <i>f</i>:<i>X</i> → <i>Y</i> is a standard coarse Lipschitz embedding, then for each <i>x</i>* ∈ Lip<sub>0</sub>(<i>X</i>) there exist <i>α, γ</i> &gt; 0 depending only on <i>f</i> and <i>Q</i><sub><i>x</i>*</sub> ∈ Lip<sub>0</sub>(<i>Y</i>) with <span>({Vert{{Q_{{x^*}}}}Vert_{{rm{Lip}}}} le alpha {Vert {{x^*}}Vert_{{rm{Lip}}}})</span> such that </p><div><div><span>$$Vert{{Q_{{x^*}}}f(x) - {x^*}(x)}Vertle gamma {left| {{x^*}} right|_{{rm{Lip}}}},;;;;;{rm{for}};{rm{all}};x in X.$$</span></div></div><p>Coarse stability for a pair of metric spaces is studied. This can be considered as a coarse version of Qian Problem. As an application, we give candidate negative answers to a 58-year old problem by Lindenstrauss asking whether every Banach space is a Lipschitz retract of its bidual. Indeed, we show that <i>X</i> is not a Lipschitz retract of its bidual if <i>X</i> is a universally left-coarsely stable space but not an absolute cardinality-Lipschitz retract. If there exists a universally right-coarsely stable Banach space with the RNP but not isomorphic to any Hilbert space, then the problem also has a negative answer for a separable space.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50031261","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Characterization of Lipschitz Functions via Commutators of Multilinear Singular Integral Operators in Variable Lebesgue Spaces 通过可变 Lebesgue 空间中多线性奇异积分算子的换元器表征 Lipschitz 函数
IF 0.7 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2023-09-15 DOI: 10.1007/s10114-023-2164-0
Jiang Long Wu, Pu Zhang
{"title":"Characterization of Lipschitz Functions via Commutators of Multilinear Singular Integral Operators in Variable Lebesgue Spaces","authors":"Jiang Long Wu,&nbsp;Pu Zhang","doi":"10.1007/s10114-023-2164-0","DOIUrl":"10.1007/s10114-023-2164-0","url":null,"abstract":"<div><p>Let <span>(overrightarrow{b}=(b_{1},b_{2},ldots,b_{m}))</span> be a collection of locally integrable functions and <span>(T_{Sigmaoverrightarrow{b}})</span> the commutator of multilinear singular integral operator <i>T</i>. Denote by <span>(mathbb{L}(delta))</span> and <span>(mathbb{L}(delta(cdot)))</span> the Lipschitz spaces and the variable Lipschitz spaces, respectively. The main purpose of this paper is to establish some new characterizations of the (variable) Lipschitz spaces in terms of the boundedness of multilinear commutator <span>(T_{Sigmaoverrightarrow{b}})</span> in the context of the variable exponent Lebesgue spaces, that is, the authors give the necessary and sufficient conditions for <i>b</i><sub><i>j</i></sub> (<i>j</i> = 1, 2, …, <i>m</i>) to be <span>(mathbb{L}(delta))</span> or <span>(mathbb{L}(delta(cdot)))</span> via the boundedness of multilinear commutator from products of variable exponent Lebesgue spaces to variable exponent Lebesgue spaces. The authors do so by applying the Fourier series technique and some pointwise estimate for the commutators. The key tool in obtaining such pointwise estimate is a certain generalization of the classical sharp maximal operator.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135352770","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Variational Analysis Based on Proximal Subdifferential on Smooth Banach Spaces 光滑Banach空间上基于近次微分的变分分析
3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2023-09-15 DOI: 10.1007/s10114-023-2439-5
Xi Yin Zheng
{"title":"Variational Analysis Based on Proximal Subdifferential on Smooth Banach Spaces","authors":"Xi Yin Zheng","doi":"10.1007/s10114-023-2439-5","DOIUrl":"https://doi.org/10.1007/s10114-023-2439-5","url":null,"abstract":"","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135438140","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Scattering for the Radial Schrödinger Equation with Combined Power-type and Choquard-type Nonlinearities 结合幂型和脉弦型非线性的径向Schrödinger方程的散射
3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2023-09-15 DOI: 10.1007/s10114-023-2570-3
Ying Wang, Cheng Bin Xu
{"title":"Scattering for the Radial Schrödinger Equation with Combined Power-type and Choquard-type Nonlinearities","authors":"Ying Wang, Cheng Bin Xu","doi":"10.1007/s10114-023-2570-3","DOIUrl":"https://doi.org/10.1007/s10114-023-2570-3","url":null,"abstract":"","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135484767","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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