Pub Date : 2023-10-01DOI: 10.14321/realanalexch.48.2.1671696175
Anthony Gauvan
We generalize Mitsis’s work to higher dimensions and give application to a conditional estimate concerning Omega-Kakeya sets. Also, following Bourgain's arithmetic argument, we improve concrete bound on the Hausdorff dimension of an Omega-Kakeya set.
{"title":"Norm Estimates for the Kakeya Maximal Function in High Dimensions with Respect to General Measures","authors":"Anthony Gauvan","doi":"10.14321/realanalexch.48.2.1671696175","DOIUrl":"https://doi.org/10.14321/realanalexch.48.2.1671696175","url":null,"abstract":"We generalize Mitsis’s work to higher dimensions and give application to a conditional estimate concerning Omega-Kakeya sets. Also, following Bourgain's arithmetic argument, we improve concrete bound on the Hausdorff dimension of an Omega-Kakeya set.","PeriodicalId":44674,"journal":{"name":"Real Analysis Exchange","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134979042","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}
Pub Date : 2023-10-01DOI: 10.14321/realanalexch.48.2.1645609092
Adam R. B. Erickson
Let $(X,mathcal{F},mu,T)$ be a not necessarily invertible non-atomic measure-preserving dynamical system where the $sigma$-algebra $mathcal{F}$ is generated by the intervals according to some total order. The main result is that the classical Rokhlin lemma may be adapted to such a situation assuming a slight extension of aperiodicity. This result is compared to previous noninvertible versions of the Rokhlin lemma.
{"title":"A Rokhlin Lemma for Noninvertible Totally-Ordered Measure-Preserving Dynamical Systems","authors":"Adam R. B. Erickson","doi":"10.14321/realanalexch.48.2.1645609092","DOIUrl":"https://doi.org/10.14321/realanalexch.48.2.1645609092","url":null,"abstract":"Let $(X,mathcal{F},mu,T)$ be a not necessarily invertible non-atomic measure-preserving dynamical system where the $sigma$-algebra $mathcal{F}$ is generated by the intervals according to some total order. The main result is that the classical Rokhlin lemma may be adapted to such a situation assuming a slight extension of aperiodicity. This result is compared to previous noninvertible versions of the Rokhlin lemma.","PeriodicalId":44674,"journal":{"name":"Real Analysis Exchange","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134979036","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}
Pub Date : 2023-10-01DOI: 10.14321/realanalexch.48.2.1643257005
Juan Carlos Sampedro
A construction of product measures is given for an arbitrary sequence of measure spaces via outer measure techniques without imposing any condition on the underlying measure spaces. This result generalizes the ones given up to date.
{"title":"Existence of Infinite Product Measures","authors":"Juan Carlos Sampedro","doi":"10.14321/realanalexch.48.2.1643257005","DOIUrl":"https://doi.org/10.14321/realanalexch.48.2.1643257005","url":null,"abstract":"A construction of product measures is given for an arbitrary sequence of measure spaces via outer measure techniques without imposing any condition on the underlying measure spaces. This result generalizes the ones given up to date.","PeriodicalId":44674,"journal":{"name":"Real Analysis Exchange","volume":"155 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134979037","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}
Pub Date : 2023-10-01DOI: 10.14321/realanalexch.48.2.1674501193
David Walmsley
{"title":"Hypercyclic Algebras for Convolution Operators with Long Arithmetic Progressions in their Zero Sets","authors":"David Walmsley","doi":"10.14321/realanalexch.48.2.1674501193","DOIUrl":"https://doi.org/10.14321/realanalexch.48.2.1674501193","url":null,"abstract":"","PeriodicalId":44674,"journal":{"name":"Real Analysis Exchange","volume":"44 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134979045","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}
Pub Date : 2023-01-01DOI: 10.14321/realanalexch.48.1.1660633299
A. Batal, Sadık Eyidoğan, H. Göral
{"title":"Irreducibility and Primality in Differentiability Classes","authors":"A. Batal, Sadık Eyidoğan, H. Göral","doi":"10.14321/realanalexch.48.1.1660633299","DOIUrl":"https://doi.org/10.14321/realanalexch.48.1.1660633299","url":null,"abstract":"","PeriodicalId":44674,"journal":{"name":"Real Analysis Exchange","volume":"1 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66984402","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}
Pub Date : 2023-01-01DOI: 10.14321/realanalexch.48.1.1661058123
Oleksiy Karlovych, E. Shargorodsky
{"title":"Remark on Singular Integral Operators of Convolution Type on Rearrangement-Invariant Banach Function Spaces","authors":"Oleksiy Karlovych, E. Shargorodsky","doi":"10.14321/realanalexch.48.1.1661058123","DOIUrl":"https://doi.org/10.14321/realanalexch.48.1.1661058123","url":null,"abstract":"","PeriodicalId":44674,"journal":{"name":"Real Analysis Exchange","volume":"1 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66984527","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}
Pub Date : 2023-01-01DOI: 10.14321/realanalexch.48.1.1659420505
L. Snoha
{"title":"The Life and Mathematics of Jaroslav Smítal","authors":"L. Snoha","doi":"10.14321/realanalexch.48.1.1659420505","DOIUrl":"https://doi.org/10.14321/realanalexch.48.1.1659420505","url":null,"abstract":"","PeriodicalId":44674,"journal":{"name":"Real Analysis Exchange","volume":"1 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66984655","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}
Pub Date : 2023-01-01DOI: 10.14321/realanalexch.48.1.1659420745
Michaela Mlíchová
{"title":"Recollections about Jaroslav Smítal","authors":"Michaela Mlíchová","doi":"10.14321/realanalexch.48.1.1659420745","DOIUrl":"https://doi.org/10.14321/realanalexch.48.1.1659420745","url":null,"abstract":"","PeriodicalId":44674,"journal":{"name":"Real Analysis Exchange","volume":"1 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66984758","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}
Pub Date : 2023-01-01DOI: 10.14321/realanalexch.48.1.1654398223
I. Blahota
{"title":"Approximation by Subsequences of Matrix Transform Mean of Walsh-Fourier Series","authors":"I. Blahota","doi":"10.14321/realanalexch.48.1.1654398223","DOIUrl":"https://doi.org/10.14321/realanalexch.48.1.1654398223","url":null,"abstract":"","PeriodicalId":44674,"journal":{"name":"Real Analysis Exchange","volume":"1 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66984282","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}
Pub Date : 2023-01-01DOI: 10.14321/realanalexch.48.1.1643688157
S. Majumdar
{"title":"Extension of the Continuity Theorems of Lebesgue Integration","authors":"S. Majumdar","doi":"10.14321/realanalexch.48.1.1643688157","DOIUrl":"https://doi.org/10.14321/realanalexch.48.1.1643688157","url":null,"abstract":"","PeriodicalId":44674,"journal":{"name":"Real Analysis Exchange","volume":"1 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66983917","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}
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