{"title":"Characterizations of local $A_{infty}$ weights and applications to local singular integrals","authors":"Federico Campos, Oscar Salinas, Beatriz Viviani","doi":"10.33044/revuma.4355","DOIUrl":"https://doi.org/10.33044/revuma.4355","url":null,"abstract":"","PeriodicalId":54469,"journal":{"name":"Revista De La Union Matematica Argentina","volume":"100 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136236452","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We give a simpler proof of the Gagliardo estimate with a measure obtained by Franchi, Pérez, and Wheeden [Proc. London Math. Soc. (3) 80 no. 3 (2000), 665–689], and improved by Pérez and Rela [Trans. Amer. Math. Soc. 372 no. 9 (2019), 6087–6133]. This result will be further improved using fractional Poincaré type inequalities with the extra bonus of Bourgain– Brezis–Mironescu as done by Hurri-Syrjänen, Mart́ınez-Perales, Pérez, and Vähäkangas [Internat. Math. Res. Notices (2022), rnac246] with a new argument. This will be used with the HMS extrapolation theorem to get Lp type result. 1. The isoperimetric inequality and extrapolation theory It is a great pleasure for us to dedicate this article to Eleonor Harboure, Pola, who played a central role in the development of modern Harmonic Analysis in Argentina. The first author is deeply grateful for her kind support during early stages of his career. Both authors want to stress how influential the work of Pola was to the mathematical community. This paper is also a tribute to the extrapolation theorem of Pola, R. Maćıas, and C. Segovia which was published in the American Journal of Mathematics [21] (see also [20]). See Theorem 2.1 in Section 2 for an updated version. We will refer to it as the HMS extrapolation theorem. Thanks to this result we can complete some of the main results obtained in [32] in the classical setting. A fractional counterpart with the Bourgain–Brezis–Mironescu gain will be obtained in the line of results as derived in [22] or [3]. The HMS extrapolation theorem was inspired by the classical extrapolation theorem of Rubio de Francia [8, 10,18]. 2020 Mathematics Subject Classification. Primary 42B25; Secondary 42B20. C. P. was supported by grant PID2020-113156GB-I00, Spanish Government; by the Basque Government through grant IT1615-22 and the BERC 2014-2017 program; and by BCAM Severo Ochoa accreditation SEV-2013-0323, Spanish Government. He is also very grateful to the MittagLeffler Institute under the program “Geometric aspects of nonlinear partial differential equations” where part of this research was carried out. E. R. was supported the projects PICT 2019-03968, PICT 2018-3399 and UBACyT 20020190200230BA. He is also very grateful to the suuport from Guandgdong Technion Israel Institute of Technology where part of this research was carried out.
{"title":"A tribute to Pola Harboure: Isoperimetric inequalities and the HMS extrapolation theorem","authors":"Carlos Pérez, Ezequiel Rela","doi":"10.33044/revuma.4356","DOIUrl":"https://doi.org/10.33044/revuma.4356","url":null,"abstract":"We give a simpler proof of the Gagliardo estimate with a measure obtained by Franchi, Pérez, and Wheeden [Proc. London Math. Soc. (3) 80 no. 3 (2000), 665–689], and improved by Pérez and Rela [Trans. Amer. Math. Soc. 372 no. 9 (2019), 6087–6133]. This result will be further improved using fractional Poincaré type inequalities with the extra bonus of Bourgain– Brezis–Mironescu as done by Hurri-Syrjänen, Mart́ınez-Perales, Pérez, and Vähäkangas [Internat. Math. Res. Notices (2022), rnac246] with a new argument. This will be used with the HMS extrapolation theorem to get Lp type result. 1. The isoperimetric inequality and extrapolation theory It is a great pleasure for us to dedicate this article to Eleonor Harboure, Pola, who played a central role in the development of modern Harmonic Analysis in Argentina. The first author is deeply grateful for her kind support during early stages of his career. Both authors want to stress how influential the work of Pola was to the mathematical community. This paper is also a tribute to the extrapolation theorem of Pola, R. Maćıas, and C. Segovia which was published in the American Journal of Mathematics [21] (see also [20]). See Theorem 2.1 in Section 2 for an updated version. We will refer to it as the HMS extrapolation theorem. Thanks to this result we can complete some of the main results obtained in [32] in the classical setting. A fractional counterpart with the Bourgain–Brezis–Mironescu gain will be obtained in the line of results as derived in [22] or [3]. The HMS extrapolation theorem was inspired by the classical extrapolation theorem of Rubio de Francia [8, 10,18]. 2020 Mathematics Subject Classification. Primary 42B25; Secondary 42B20. C. P. was supported by grant PID2020-113156GB-I00, Spanish Government; by the Basque Government through grant IT1615-22 and the BERC 2014-2017 program; and by BCAM Severo Ochoa accreditation SEV-2013-0323, Spanish Government. He is also very grateful to the MittagLeffler Institute under the program “Geometric aspects of nonlinear partial differential equations” where part of this research was carried out. E. R. was supported the projects PICT 2019-03968, PICT 2018-3399 and UBACyT 20020190200230BA. He is also very grateful to the suuport from Guandgdong Technion Israel Institute of Technology where part of this research was carried out.","PeriodicalId":54469,"journal":{"name":"Revista De La Union Matematica Argentina","volume":"91 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136235951","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
. In this work we consider the Littlewood–Paley quadratic function associated to the Schr¨odinger operator L = − ∆ + V involving spatial derivatives of the semigroup’s kernel. Under an appropriate reverse-H¨older condition on the potential we show boundedness on weighted L p spaces for 1 < p < p 0 , where p 0 depends on the order of the reverse-H¨older property. Using a subordination formula we extend these results to the corresponding quadratic function associated to the semigroup related to L α , 0 < α < 1.
{"title":"Vertical Littlewood–Paley functions related to a Schrödinger operator","authors":"Bruno Bongioanni, Eleonor Harboure, Pablo Quijano","doi":"10.33044/revuma.4381","DOIUrl":"https://doi.org/10.33044/revuma.4381","url":null,"abstract":". In this work we consider the Littlewood–Paley quadratic function associated to the Schr¨odinger operator L = − ∆ + V involving spatial derivatives of the semigroup’s kernel. Under an appropriate reverse-H¨older condition on the potential we show boundedness on weighted L p spaces for 1 < p < p 0 , where p 0 depends on the order of the reverse-H¨older property. Using a subordination formula we extend these results to the corresponding quadratic function associated to the semigroup related to L α , 0 < α < 1.","PeriodicalId":54469,"journal":{"name":"Revista De La Union Matematica Argentina","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136236103","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
When $L$ is the Hermite or the Ornstein-Uhlenbeck operator, we find minimal integrability and smoothness conditions on a function $f$ so that the fractional power $L^sigma f(x_0)$ is well-defined at a given point $x_0$. We illustrate the optimality of the conditions with various examples. Finally, we obtain similar results for the fractional operators $(-Delta+R)^sigma$, with $R>0$.
{"title":"Pointwise convergence of fractional powers of Hermite type operators","authors":"Guillermo Flores, Gustavo Garrigós, Teresa Signes, Beatriz Viviani","doi":"10.33044/revuma.4357","DOIUrl":"https://doi.org/10.33044/revuma.4357","url":null,"abstract":"When $L$ is the Hermite or the Ornstein-Uhlenbeck operator, we find minimal integrability and smoothness conditions on a function $f$ so that the fractional power $L^sigma f(x_0)$ is well-defined at a given point $x_0$. We illustrate the optimality of the conditions with various examples. Finally, we obtain similar results for the fractional operators $(-Delta+R)^sigma$, with $R>0$.","PeriodicalId":54469,"journal":{"name":"Revista De La Union Matematica Argentina","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136153371","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Tishbe Pilarh Herrera-Ramírez, Andrés Fraguela-Collar, Jorge Velázquez-Castro, Carlos Antonio Abella-Medrano
{"title":"Mathematical model for the aquatic stage of <i>Aedes aegypti</i> considering variable egg-hatching rate and inter-specific competition between larval stages","authors":"Tishbe Pilarh Herrera-Ramírez, Andrés Fraguela-Collar, Jorge Velázquez-Castro, Carlos Antonio Abella-Medrano","doi":"10.33044/revuma.3067","DOIUrl":"https://doi.org/10.33044/revuma.3067","url":null,"abstract":"","PeriodicalId":54469,"journal":{"name":"Revista De La Union Matematica Argentina","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136249328","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This survey builds on the two surveys by Wang and Lauret written almost a decade ago to give the current state of affairs regarding homogeneous Einstein spaces.
{"title":"Survey: Homogeneous Einstein manifolds","authors":"Michael Jablonski","doi":"10.33044/revuma.3588","DOIUrl":"https://doi.org/10.33044/revuma.3588","url":null,"abstract":"This survey builds on the two surveys by Wang and Lauret written almost a decade ago to give the current state of affairs regarding homogeneous Einstein spaces.","PeriodicalId":54469,"journal":{"name":"Revista De La Union Matematica Argentina","volume":"66 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135236030","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
. We present a survey of results concerning arithmetic properties of generalized Fibonacci sequences and certain Diophantine equations involving terms from that family of numbers. Most of these results have been recently obtained by the research groups in number theory at the Universities of Cauca (in Popay´an) and of Valle (in Cali), Colombia, lead by the first two authors.
{"title":"Arithmetic properties of generalized Fibonacci numbers","authors":"Jhon J. Bravo, C. A. Gómez, F. Luca","doi":"10.33044/revuma.2937","DOIUrl":"https://doi.org/10.33044/revuma.2937","url":null,"abstract":". We present a survey of results concerning arithmetic properties of generalized Fibonacci sequences and certain Diophantine equations involving terms from that family of numbers. Most of these results have been recently obtained by the research groups in number theory at the Universities of Cauca (in Popay´an) and of Valle (in Cali), Colombia, lead by the first two authors.","PeriodicalId":54469,"journal":{"name":"Revista De La Union Matematica Argentina","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48061079","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
. For a Duffing-type oscillator with constant damping, a unique odd nonlinearity, and time-dependent coefficients which are quasi-periodic, we prove existence and stability conditions of quasi-periodic solutions. We thus generalize some results for periodic coefficients and quintic nonlinearity. We use the classical theory of perturbations and present some numerical examples for the quintic case to illustrate our findings.
{"title":"Stable quasi-periodic orbits of a class of quintic Duffing systems","authors":"H. Díaz-Marín, O. Osuna","doi":"10.33044/revuma.2829","DOIUrl":"https://doi.org/10.33044/revuma.2829","url":null,"abstract":". For a Duffing-type oscillator with constant damping, a unique odd nonlinearity, and time-dependent coefficients which are quasi-periodic, we prove existence and stability conditions of quasi-periodic solutions. We thus generalize some results for periodic coefficients and quintic nonlinearity. We use the classical theory of perturbations and present some numerical examples for the quintic case to illustrate our findings.","PeriodicalId":54469,"journal":{"name":"Revista De La Union Matematica Argentina","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43695570","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Let $K$ be a pure number field generated by a complex root of a monic irreducible polynomial $F(x)=x^{60}-min mathbb{Z}[x]$, with $mneq pm1$ a square free integer. In this paper, we study the monogeneity of $K$. We prove that if $mnotequiv 1md{4}$, $mnotequiv mp 1 md{9} $ and $overline{m}notin{mp 1,mp 7} md{25}$, then $K$ is monogenic. But if $mequiv 1md{4}$, $mequiv mp1 md{9}$, or $mequiv mp 1md{25}$, then $K$ is not monogenic. Our results are illustrated by examples.
{"title":"On power integral bases of certain pure number fields defined by $x^{84}-m$","authors":"Lhoussain El Fadil, Omar Kchit, Hanan Choulli","doi":"10.33044/revuma.2836","DOIUrl":"https://doi.org/10.33044/revuma.2836","url":null,"abstract":"Let $K$ be a pure number field generated by a complex root of a monic irreducible polynomial $F(x)=x^{60}-min mathbb{Z}[x]$, with $mneq pm1$ a square free integer. In this paper, we study the monogeneity of $K$. We prove that if $mnotequiv 1md{4}$, $mnotequiv mp 1 md{9} $ and $overline{m}notin{mp 1,mp 7} md{25}$, then $K$ is monogenic. But if $mequiv 1md{4}$, $mequiv mp1 md{9}$, or $mequiv mp 1md{25}$, then $K$ is not monogenic. Our results are illustrated by examples.","PeriodicalId":54469,"journal":{"name":"Revista De La Union Matematica Argentina","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135210673","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
. Let a,b,c be integers. We provide a necessary condition for the function | ax 2 + bx + c | to generate only primes for consecutive integers. We then apply this criterion to give sufficient conditions for the real quadratic field K = Q ( √ d ), d ∈ N , to have class number one, in terms of prime-producing quadratic polynomials.
{"title":"Prime-generating quadratic polynomials","authors":"Víctor Julio Ramírez Viñas","doi":"10.33044/revuma.2571","DOIUrl":"https://doi.org/10.33044/revuma.2571","url":null,"abstract":". Let a,b,c be integers. We provide a necessary condition for the function | ax 2 + bx + c | to generate only primes for consecutive integers. We then apply this criterion to give sufficient conditions for the real quadratic field K = Q ( √ d ), d ∈ N , to have class number one, in terms of prime-producing quadratic polynomials.","PeriodicalId":54469,"journal":{"name":"Revista De La Union Matematica Argentina","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48779705","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：