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Best Local Weighted Approximation. An Approach with Abstract Seminorms 最佳局部加权近似。抽象半模的一种方法
IF 0.2
Real Analysis Exchange Pub Date : 2020-11-01 DOI: 10.14321/REALANALEXCH.45.2.0265
C. Ridolfi
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引用次数: 0
Asymptotic Constants in Averaged Hölder Inequalities 平均Hölder不等式中的渐近常数
IF 0.2
Real Analysis Exchange Pub Date : 2020-11-01 DOI: 10.14321/REALANALEXCH.45.2.0425
G. Herzog, P. Kunstmann
{"title":"Asymptotic Constants in Averaged Hölder Inequalities","authors":"G. Herzog, P. Kunstmann","doi":"10.14321/REALANALEXCH.45.2.0425","DOIUrl":"https://doi.org/10.14321/REALANALEXCH.45.2.0425","url":null,"abstract":"","PeriodicalId":44674,"journal":{"name":"Real Analysis Exchange","volume":" ","pages":""},"PeriodicalIF":0.2,"publicationDate":"2020-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42714435","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Non-Differentiability of the Convolution of Differentiable Real Functions 可微实函数卷积的不可微性
IF 0.2
Real Analysis Exchange Pub Date : 2020-11-01 DOI: 10.14321/REALANALEXCH.45.2.0327
K. Ciesielski, P. Jiménez-Rodríguez, G. A. Muñoz-Fernández, J. Seoane-Sepúlveda
{"title":"Non-Differentiability of the Convolution of Differentiable Real Functions","authors":"K. Ciesielski, P. Jiménez-Rodríguez, G. A. Muñoz-Fernández, J. Seoane-Sepúlveda","doi":"10.14321/REALANALEXCH.45.2.0327","DOIUrl":"https://doi.org/10.14321/REALANALEXCH.45.2.0327","url":null,"abstract":"","PeriodicalId":44674,"journal":{"name":"Real Analysis Exchange","volume":" ","pages":""},"PeriodicalIF":0.2,"publicationDate":"2020-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43593109","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Decomposition for Borel Measures (mu le mathcal{H}^{s}) Borel测度的分解 (mu le mathcal{H}^{s})
IF 0.2
Real Analysis Exchange Pub Date : 2020-10-29 DOI: 10.14321/realanalexch.48.1.1629953964
Antoine Detaille, A. Ponce
{"title":"A Decomposition for Borel Measures (mu le mathcal{H}^{s})","authors":"Antoine Detaille, A. Ponce","doi":"10.14321/realanalexch.48.1.1629953964","DOIUrl":"https://doi.org/10.14321/realanalexch.48.1.1629953964","url":null,"abstract":"We prove that every finite Borel measure $mu$ in $mathbb{R}^N$ that is bounded from above by the Hausdorff measure $mathcal{H}^s$ can be split in countable many parts $mulfloor_{E_k}$ that are bounded from above by the Hausdorff content $mathcal{H}_infty^s$. Such a result generalises a theorem due to R. Delaware that says that any Borel set with finite Hausdorff measure can be decomposed as a countable disjoint union of straight sets. We also investigate the case where $mu$ is not necessarily finite.","PeriodicalId":44674,"journal":{"name":"Real Analysis Exchange","volume":"1 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2020-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42390262","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Lipschitz Homotopy Groups of Contact 3-Manifolds 接触3-流形的Lipschitz同态群
IF 0.2
Real Analysis Exchange Pub Date : 2020-08-16 DOI: 10.14321/realanalexch.47.1.1598582300
Daniel Perry
{"title":"Lipschitz Homotopy Groups of Contact 3-Manifolds","authors":"Daniel Perry","doi":"10.14321/realanalexch.47.1.1598582300","DOIUrl":"https://doi.org/10.14321/realanalexch.47.1.1598582300","url":null,"abstract":"We study contact 3-manifolds using the techniques of sub-Riemannian geometry and geometric measure theory, in particular establishing properties of their Lipschitz homotopy groups. We prove a biLipschitz version of the Theorem of Darboux: a contact $(2n+1)$-manifold endowed with a sub-Riemannian structure is locally biLipschitz equivalent to the Heisenberg group $mathbb{H}^n$ with its Carnot-Caratheodory metric. Then each contact $(2n+1)$-manifold endowed with a sub-Riemannian structure is purely $k$-unrectifiable for $k>n$. We extend results of Dejarnette et al. (arXiv:1109.4641 [math.FA]) and Wenger and Young (arXiv:1210.6943 [math.GT]) by showing for any purely 2-unrectifiable sub-Riemannian manifold $(M,xi,g)$ that the $n$th Lipschitz homotopy group is trivial for $ngeq2$ and that the set of oriented, horizontal knots in $(M,xi)$ injects into the first Lipschitz homotopy group. Thus, the first Lipschitz homotopy group of any contact 3-manifold is uncountably generated. Therefore, in the sense of Lipschitz homotopy groups, a contact 3-manifold is a $K(pi,1)$-space for an uncountably generated group $pi$. Finally, we prove that each open distributional embedding between purely 2-unrectifiable sub-Riemannian manifolds induces an injective map on the associated first Lipschitz homotopy groups. Therefore, each open subset of a contact 3-manifold determines an uncountable subgroup of the first Lipschitz homotopy group of the contact 3-manifold.","PeriodicalId":44674,"journal":{"name":"Real Analysis Exchange","volume":" ","pages":""},"PeriodicalIF":0.2,"publicationDate":"2020-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44399263","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
A girsanov result for the pettis integral petis积分的一个girsanov结果
IF 0.2
Real Analysis Exchange Pub Date : 2020-07-09 DOI: 10.14321/realanalexch.46.1.0175
D. Candeloro, A. R. Sambucini, Luca Trastulli
{"title":"A girsanov result for the pettis integral","authors":"D. Candeloro, A. R. Sambucini, Luca Trastulli","doi":"10.14321/realanalexch.46.1.0175","DOIUrl":"https://doi.org/10.14321/realanalexch.46.1.0175","url":null,"abstract":"A kind of Pettis integral representation for a Banach valued Ito process is given and its drift term is modified using a Girsanov Theorem.","PeriodicalId":44674,"journal":{"name":"Real Analysis Exchange","volume":" ","pages":""},"PeriodicalIF":0.2,"publicationDate":"2020-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49308766","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
ON HÖLDER MAPS AND PRIME GAPS 在hÖlder地图和主要缺口上
IF 0.2
Real Analysis Exchange Pub Date : 2020-06-17 DOI: 10.14321/REALANALEXCH.46.2.0523
Haipeng Chen, J. Fraser
{"title":"ON HÖLDER MAPS AND PRIME GAPS","authors":"Haipeng Chen, J. Fraser","doi":"10.14321/REALANALEXCH.46.2.0523","DOIUrl":"https://doi.org/10.14321/REALANALEXCH.46.2.0523","url":null,"abstract":"Let $p_n$ denote the $n$th prime, and consider the function $1/n mapsto 1/p_n$ which maps the reciprocals of the positive integers bijectively to the reciprocals of the primes. We show that Holder continuity of this function is equivalent to a parameterised family of Cramer type estimates on the gaps between successive primes. Here the parameterisation comes from the Holder exponent. In particular, we show that Cramer's conjecture is equivalent to the map $1/n mapsto 1/p_n$ being Lipschitz. On the other hand, we show that the inverse map $1/p_n mapsto 1/n$ is Holder of all orders but not Lipshitz and this is independent of Cramer's conjecture.","PeriodicalId":44674,"journal":{"name":"Real Analysis Exchange","volume":" ","pages":""},"PeriodicalIF":0.2,"publicationDate":"2020-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42549915","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Change of Variable Formulas for Riemann Integrals 黎曼积分的变量变换公式
IF 0.2
Real Analysis Exchange Pub Date : 2020-05-01 DOI: 10.14321/realanalexch.45.1.0151
A. Torchinsky
{"title":"Change of Variable Formulas for Riemann Integrals","authors":"A. Torchinsky","doi":"10.14321/realanalexch.45.1.0151","DOIUrl":"https://doi.org/10.14321/realanalexch.45.1.0151","url":null,"abstract":"","PeriodicalId":44674,"journal":{"name":"Real Analysis Exchange","volume":"45 1","pages":"151-172"},"PeriodicalIF":0.2,"publicationDate":"2020-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42267302","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Commutators, BMO, Hardy Spaces and Factorization: A Survey 交换子、BMO、Hardy空间和因子分解:综述
IF 0.2
Real Analysis Exchange Pub Date : 2020-05-01 DOI: 10.14321/realanalexch.45.1.0001
B. Wick
{"title":"Commutators, BMO, Hardy Spaces and Factorization: A Survey","authors":"B. Wick","doi":"10.14321/realanalexch.45.1.0001","DOIUrl":"https://doi.org/10.14321/realanalexch.45.1.0001","url":null,"abstract":"","PeriodicalId":44674,"journal":{"name":"Real Analysis Exchange","volume":"45 1","pages":"1-28"},"PeriodicalIF":0.2,"publicationDate":"2020-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49313732","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Double Lusin Condition and Convergence Theorems for the Backwards Itô-Henstock Integral 逆Itô-Henstock积分的二重Lusin条件和收敛定理
IF 0.2
Real Analysis Exchange Pub Date : 2020-05-01 DOI: 10.14321/realanalexch.45.1.0101
Ricky F. Rulete, M. A. Labendia
{"title":"Double Lusin Condition and Convergence Theorems for the Backwards Itô-Henstock Integral","authors":"Ricky F. Rulete, M. A. Labendia","doi":"10.14321/realanalexch.45.1.0101","DOIUrl":"https://doi.org/10.14321/realanalexch.45.1.0101","url":null,"abstract":"","PeriodicalId":44674,"journal":{"name":"Real Analysis Exchange","volume":"45 1","pages":"101-126"},"PeriodicalIF":0.2,"publicationDate":"2020-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46109773","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
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