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Analysis and Geometry in Metric Spaces最新文献

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Comparison Theorems on Weighted Finsler Manifolds and Spacetimes with ϵ-Range 关于加权Finsler流形与具有ε-范围的时空的比较定理
IF 1 3区 数学
Analysis and Geometry in Metric Spaces Pub Date : 2020-07-01 DOI: 10.1515/agms-2020-0131
Yufeng Lu, E. Minguzzi, Shin-ichi Ohta
{"title":"Comparison Theorems on Weighted Finsler Manifolds and Spacetimes with ϵ-Range","authors":"Yufeng Lu, E. Minguzzi, Shin-ichi Ohta","doi":"10.1515/agms-2020-0131","DOIUrl":"https://doi.org/10.1515/agms-2020-0131","url":null,"abstract":"Abstract We establish the Bonnet–Myers theorem, Laplacian comparison theorem, and Bishop–Gromov volume comparison theorem for weighted Finsler manifolds as well as weighted Finsler spacetimes, of weighted Ricci curvature bounded below by using the weight function. These comparison theorems are formulated with ϵ-range introduced in our previous paper, that provides a natural viewpoint of interpolating weighted Ricci curvature conditions of different effective dimensions. Some of our results are new even for weighted Riemannian manifolds and generalize comparison theorems of Wylie–Yeroshkin and Kuwae–Li.","PeriodicalId":48637,"journal":{"name":"Analysis and Geometry in Metric Spaces","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2020-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46594336","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: 14
Asymptotically Mean Value Harmonic Functions in Doubling Metric Measure Spaces 双度量测度空间中的渐近均值调和函数
IF 1 3区 数学
Analysis and Geometry in Metric Spaces Pub Date : 2020-05-28 DOI: 10.1515/agms-2022-0143
Tomasz Adamowicz, Antoni Kijowski, Elefterios Soultanis
{"title":"Asymptotically Mean Value Harmonic Functions in Doubling Metric Measure Spaces","authors":"Tomasz Adamowicz, Antoni Kijowski, Elefterios Soultanis","doi":"10.1515/agms-2022-0143","DOIUrl":"https://doi.org/10.1515/agms-2022-0143","url":null,"abstract":"Abstract We consider functions with an asymptotic mean value property, known to characterize harmonicity in Riemannian manifolds and in doubling metric measure spaces. We show that the strongly amv-harmonic functions are Hölder continuous for any exponent below one. More generally, we define the class of functions with finite amv-norm and show that functions in this class belong to a fractional Hajłasz–Sobolev space and their blow-ups satisfy the mean-value property. Furthermore, in the weighted Euclidean setting we find an elliptic PDE satisfied by amv-harmonic functions.","PeriodicalId":48637,"journal":{"name":"Analysis and Geometry in Metric Spaces","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2020-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41703174","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: 3
On the Volume of Sections of the Cube 关于立方体截面的体积
IF 1 3区 数学
Analysis and Geometry in Metric Spaces Pub Date : 2020-04-06 DOI: 10.1515/agms-2020-0103
G. Ivanov, Igor Tsiutsiurupa
{"title":"On the Volume of Sections of the Cube","authors":"G. Ivanov, Igor Tsiutsiurupa","doi":"10.1515/agms-2020-0103","DOIUrl":"https://doi.org/10.1515/agms-2020-0103","url":null,"abstract":"Abstract We study the properties of the maximal volume k-dimensional sections of the n-dimensional cube [−1, 1]n. We obtain a first order necessary condition for a k-dimensional subspace to be a local maximizer of the volume of such sections, which we formulate in a geometric way. We estimate the length of the projection of a vector of the standard basis of ℝn onto a k-dimensional subspace that maximizes the volume of the intersection. We find the optimal upper bound on the volume of a planar section of the cube [−1, 1]n, n ≥ 2.","PeriodicalId":48637,"journal":{"name":"Analysis and Geometry in Metric Spaces","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2020-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/agms-2020-0103","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43580017","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: 10
BMO and the John-Nirenberg Inequality on Measure Spaces 测度空间上的BMO和John-Nirenberg不等式
IF 1 3区 数学
Analysis and Geometry in Metric Spaces Pub Date : 2020-01-01 DOI: 10.1515/agms-2020-0115
G. Dafni, Ryan Gibara, Andrew Lavigne
{"title":"BMO and the John-Nirenberg Inequality on Measure Spaces","authors":"G. Dafni, Ryan Gibara, Andrew Lavigne","doi":"10.1515/agms-2020-0115","DOIUrl":"https://doi.org/10.1515/agms-2020-0115","url":null,"abstract":"Abstract We study the space BMO𝒢 (𝕏) in the general setting of a measure space 𝕏 with a fixed collection 𝒢 of measurable sets of positive and finite measure, consisting of functions of bounded mean oscillation on sets in 𝒢. The aim is to see how much of the familiar BMO machinery holds when metric notions have been replaced by measure-theoretic ones. In particular, three aspects of BMO are considered: its properties as a Banach space, its relation with Muckenhoupt weights, and the John-Nirenberg inequality. We give necessary and sufficient conditions on a decomposable measure space 𝕏 for BMO𝒢 (𝕏) to be a Banach space modulo constants. We also develop the notion of a Denjoy family 𝒢, which guarantees that functions in BMO𝒢 (𝕏) satisfy the John-Nirenberg inequality on the elements of 𝒢.","PeriodicalId":48637,"journal":{"name":"Analysis and Geometry in Metric Spaces","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/agms-2020-0115","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44130551","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: 2
Pointwise Multipliers on Weak Morrey Spaces 弱Morrey空间上的点乘子
IF 1 3区 数学
Analysis and Geometry in Metric Spaces Pub Date : 2020-01-01 DOI: 10.1515/AGMS-2020-0119
Ryota Kawasumi, E. Nakai
{"title":"Pointwise Multipliers on Weak Morrey Spaces","authors":"Ryota Kawasumi, E. Nakai","doi":"10.1515/AGMS-2020-0119","DOIUrl":"https://doi.org/10.1515/AGMS-2020-0119","url":null,"abstract":"Abstract We consider generalized weak Morrey spaces with variable growth condition on spaces of homogeneous type and characterize the pointwise multipliers from a generalized weak Morrey space to another one. The set of all pointwise multipliers from a weak Lebesgue space to another one is also a weak Lebesgue space. However, we point out that the weak Morrey spaces do not always have this property just as the Morrey spaces not always.","PeriodicalId":48637,"journal":{"name":"Analysis and Geometry in Metric Spaces","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/AGMS-2020-0119","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44659983","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: 5
Embeddings between Triebel-Lizorkin Spaces on Metric Spaces Associated with Operators 算子相关度量空间上Triebel-Lizorkin空间之间的嵌入
IF 1 3区 数学
Analysis and Geometry in Metric Spaces Pub Date : 2020-01-01 DOI: 10.1515/agms-2020-0120
A. G. Georgiadis, G. Kyriazis
{"title":"Embeddings between Triebel-Lizorkin Spaces on Metric Spaces Associated with Operators","authors":"A. G. Georgiadis, G. Kyriazis","doi":"10.1515/agms-2020-0120","DOIUrl":"https://doi.org/10.1515/agms-2020-0120","url":null,"abstract":"Abstract We consider the general framework of a metric measure space satisfying the doubling volume property, associated with a non-negative self-adjoint operator, whose heat kernel enjoys standard Gaussian localization. We prove embedding theorems between Triebel-Lizorkin spaces associated with operators. Embeddings for non-classical Triebel-Lizorkin and (both classical and non-classical) Besov spaces are proved as well. Our result generalize the Euclidean case and are new for many settings of independent interest such as the ball, the interval and Riemannian manifolds.","PeriodicalId":48637,"journal":{"name":"Analysis and Geometry in Metric Spaces","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/agms-2020-0120","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41650830","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: 5
Intermediate Value Property for the Assouad Dimension of Measures 测度关联维数的中间值性质
IF 1 3区 数学
Analysis and Geometry in Metric Spaces Pub Date : 2020-01-01 DOI: 10.1515/agms-2020-0106
Ville Suomala
{"title":"Intermediate Value Property for the Assouad Dimension of Measures","authors":"Ville Suomala","doi":"10.1515/agms-2020-0106","DOIUrl":"https://doi.org/10.1515/agms-2020-0106","url":null,"abstract":"Abstract Hare, Mendivil, and Zuberman have recently shown that if X ⊂ ℝ is compact and of non-zero Assouad dimension dimA X, then for all s > dimA X, X supports measures with Assouad dimension s. We generalize this result to arbitrary complete metric spaces.","PeriodicalId":48637,"journal":{"name":"Analysis and Geometry in Metric Spaces","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/agms-2020-0106","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44963714","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
A Weak Type Vector-Valued Inequality for the Modified Hardy–Littlewood Maximal Operator for General Radon Measure on ℝn 广义Radon测度的修正Hardy-Littlewood极大算子的一个弱型向量值不等式
IF 1 3区 数学
Analysis and Geometry in Metric Spaces Pub Date : 2020-01-01 DOI: 10.1515/agms-2020-0113
Y. Sawano
{"title":"A Weak Type Vector-Valued Inequality for the Modified Hardy–Littlewood Maximal Operator for General Radon Measure on ℝn","authors":"Y. Sawano","doi":"10.1515/agms-2020-0113","DOIUrl":"https://doi.org/10.1515/agms-2020-0113","url":null,"abstract":"Abstract The aim of this paper is to prove the weak type vector-valued inequality for the modified Hardy– Littlewood maximal operator for general Radon measure on ℝn. Earlier, the strong type vector-valued inequality for the same operator and the weak type vector-valued inequality for the dyadic maximal operator were obtained. This paper will supplement these existing results by proving a weak type counterpart.","PeriodicalId":48637,"journal":{"name":"Analysis and Geometry in Metric Spaces","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/agms-2020-0113","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41761114","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
Chordal Hausdorff Convergence and Quasihyperbolic Distance Chordal-Hausdorff收敛与拟双曲距离
IF 1 3区 数学
Analysis and Geometry in Metric Spaces Pub Date : 2020-01-01 DOI: 10.1515/agms-2020-0104
D. Herron, Abigail Richard, Marie A. Snipes
{"title":"Chordal Hausdorff Convergence and Quasihyperbolic Distance","authors":"D. Herron, Abigail Richard, Marie A. Snipes","doi":"10.1515/agms-2020-0104","DOIUrl":"https://doi.org/10.1515/agms-2020-0104","url":null,"abstract":"Abstract We study Hausdorff convergence (and related topics) in the chordalization of a metric space to better understand pointed Gromov-Hausdorff convergence of quasihyperbolic distances (and other conformal distances).","PeriodicalId":48637,"journal":{"name":"Analysis and Geometry in Metric Spaces","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/agms-2020-0104","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43117965","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: 6
Complex Interpolation of Lizorkin-Triebel-Morrey Spaces on Domains Lizorkin-Triebel-Morrey空间在域上的复插值
IF 1 3区 数学
Analysis and Geometry in Metric Spaces Pub Date : 2020-01-01 DOI: 10.1515/agms-2020-0114
Ciqiang Zhuo, Marc Hovemann, W. Sickel
{"title":"Complex Interpolation of Lizorkin-Triebel-Morrey Spaces on Domains","authors":"Ciqiang Zhuo, Marc Hovemann, W. Sickel","doi":"10.1515/agms-2020-0114","DOIUrl":"https://doi.org/10.1515/agms-2020-0114","url":null,"abstract":"Abstract In this article the authors study complex interpolation of Sobolev-Morrey spaces and their generalizations, Lizorkin-Triebel-Morrey spaces. Both scales are considered on bounded domains. Under certain conditions on the parameters the outcome belongs to the scale of the so-called diamond spaces.","PeriodicalId":48637,"journal":{"name":"Analysis and Geometry in Metric Spaces","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/agms-2020-0114","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47789130","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: 9
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