{"title":"A Note on Rough Parametric Marcinkiewicz Functions","authors":"Laith Hawawsheh","doi":"10.4208/ata.oa-2017-0074","DOIUrl":"https://doi.org/10.4208/ata.oa-2017-0074","url":null,"abstract":"In this note, we obtain sharp Lp estimates of parametric Marcinkiewicz integral operators. Our result resolves a long standing open problem. Also, we present a class of parametric Marcinkiewicz integral operators that are bounded provided that their kernels belong to the sole space L1 ( Sn−1 ) .","PeriodicalId":29763,"journal":{"name":"Analysis in Theory and Applications","volume":"9 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82316667","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}
{"title":"Long Time Well-Posedness of the MHD Boundary Layer Equation in Sobolev Space","authors":"Dongxiang Chen","doi":"10.4208/ata.oa-0015","DOIUrl":"https://doi.org/10.4208/ata.oa-0015","url":null,"abstract":"In this paper, we study the long time well-posedness of 2-D MHD boundary layer equation. It was proved that if the initial data satisfies ‖(u0, h0 − 1)‖H3,0 μ ∩H1,2 μ ≤ ε, then the life span of the solution is at least of order ε2−η for η > 0.","PeriodicalId":29763,"journal":{"name":"Analysis in Theory and Applications","volume":"18 1","pages":"1-18"},"PeriodicalIF":0.6,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73286355","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}
{"title":"Inside the Light Boojums: a Journey to the Land of Boundary Defects","authors":"global sci","doi":"10.4208/ata.oa-0020","DOIUrl":"https://doi.org/10.4208/ata.oa-0020","url":null,"abstract":"","PeriodicalId":29763,"journal":{"name":"Analysis in Theory and Applications","volume":"412 1","pages":"128-160"},"PeriodicalIF":0.6,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76472299","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}
{"title":"Some Estimates of Bilinear Hausdorff Operators on Stratified Groups","authors":"global sci","doi":"10.4208/ata.oa-2019-0034","DOIUrl":"https://doi.org/10.4208/ata.oa-2019-0034","url":null,"abstract":"","PeriodicalId":29763,"journal":{"name":"Analysis in Theory and Applications","volume":"2 1","pages":"200-216"},"PeriodicalIF":0.6,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87221346","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}
{"title":"Multiple Axially Asymmetric Solutions to a Mean Field Equation on $mathbb{S}^{2}$","authors":"Zhuoran Du","doi":"10.4208/ata.oa-0016","DOIUrl":"https://doi.org/10.4208/ata.oa-0016","url":null,"abstract":"We study the following mean field equation ∆gu + ρ ( eu ∫ S2 e udμ − 1 4π ) = 0 in S2, where ρ is a real parameter. We obtain the existence of multiple axially asymmetric solutions bifurcating from u = 0 at the values ρ = 4n(n + 1)π for any odd integer n ≥ 3.","PeriodicalId":29763,"journal":{"name":"Analysis in Theory and Applications","volume":"23 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78895261","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}
{"title":"Revisit of Semi-Implicit Schemes for Phase-Field Equations","authors":"global sci","doi":"10.4208/ata.oa-su12","DOIUrl":"https://doi.org/10.4208/ata.oa-su12","url":null,"abstract":"","PeriodicalId":29763,"journal":{"name":"Analysis in Theory and Applications","volume":"71 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73661634","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}
{"title":"Estimates of Dirichlet Eigenvalues for One-Dimensional Fractal Drums","authors":"global sci","doi":"10.4208/ata.oa-su7","DOIUrl":"https://doi.org/10.4208/ata.oa-su7","url":null,"abstract":"","PeriodicalId":29763,"journal":{"name":"Analysis in Theory and Applications","volume":"44 1","pages":"243-261"},"PeriodicalIF":0.6,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79940381","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}
{"title":"A Characterization of Boundedness of Fractional Maximal Operator with Variable Kernel on Herz-Morrey Spaces","authors":"Lütfi Akın","doi":"10.4208/ata.oa-2018-1006","DOIUrl":"https://doi.org/10.4208/ata.oa-2018-1006","url":null,"abstract":"A significant number of studies have been carried out on the generalized Lebesgue spaces Lp(x), Sobolev spaces W1,p(x) and Herz spaces. In this paper, we demonstrated a characterization of boundedness of the fractional maximal operator with variable kernel on Herz-Morrey spaces.","PeriodicalId":29763,"journal":{"name":"Analysis in Theory and Applications","volume":"5 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75958284","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}
{"title":"A Note on $Card(X)$","authors":"global sci","doi":"10.4208/ata.oa-su4","DOIUrl":"https://doi.org/10.4208/ata.oa-su4","url":null,"abstract":"","PeriodicalId":29763,"journal":{"name":"Analysis in Theory and Applications","volume":"60 1","pages":"468-481"},"PeriodicalIF":0.6,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84795893","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}
{"title":"On Well-Posedness of 2D Dissipative Quasi-Geostrophic Equation in Critical Mixed Norm Lebesgue Spaces","authors":"global sci","doi":"10.4208/ata.oa-0018","DOIUrl":"https://doi.org/10.4208/ata.oa-0018","url":null,"abstract":"","PeriodicalId":29763,"journal":{"name":"Analysis in Theory and Applications","volume":"2 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85808177","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}