Pub Date : 2020-05-05DOI: 10.4310/arkiv.2021.v59.n2.a4
Georgios Dosidis, L. Grafakos
We study a family of maximal operators that provides a continuous link connecting the Hardy-Littlewood maximal function to the spherical maximal function. Our theorems are proved in the multilinear setting but may contain new results even in the linear case. For this family of operators we obtain bounds between Lebesgue spaces in the optimal range of exponents.
{"title":"On families between the Hardy–Littlewood and spherical maximal functions","authors":"Georgios Dosidis, L. Grafakos","doi":"10.4310/arkiv.2021.v59.n2.a4","DOIUrl":"https://doi.org/10.4310/arkiv.2021.v59.n2.a4","url":null,"abstract":"We study a family of maximal operators that provides a continuous link connecting the Hardy-Littlewood maximal function to the spherical maximal function. Our theorems are proved in the multilinear setting but may contain new results even in the linear case. For this family of operators we obtain bounds between Lebesgue spaces in the optimal range of exponents.","PeriodicalId":55569,"journal":{"name":"Arkiv for Matematik","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2020-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70393783","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}
Pub Date : 2020-04-05DOI: 10.4310/arkiv.2021.v59.n2.a7
J. Sjostrand, Maher Zerzeri
In this paper we study the distribution of scattering resonances for a multidimensional semi-classical Schrodinger operator, associated to a potential well in an island at energies close to the maximal one that limits the separation of the well and the surrounding sea.
{"title":"Resonances over a potential well in an island","authors":"J. Sjostrand, Maher Zerzeri","doi":"10.4310/arkiv.2021.v59.n2.a7","DOIUrl":"https://doi.org/10.4310/arkiv.2021.v59.n2.a7","url":null,"abstract":"In this paper we study the distribution of scattering resonances for a multidimensional semi-classical Schrodinger operator, associated to a potential well in an island at energies close to the maximal one that limits the separation of the well and the surrounding sea.","PeriodicalId":55569,"journal":{"name":"Arkiv for Matematik","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2020-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70393829","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 $X$ be a smooth complex projective variety. Using a construction devised to Gathmann, we present a recursive formula for some of the Gromov-Witten invariants of $X$. We prove that, when $X$ is homogeneous, this formula gives the number of osculating rational curves at a general point of a general hypersurface of $X$. This generalizes the classical well known pairs of inflexion (asymptotic) lines for surfaces in $mathbb{P}^{3}$ of Salmon, as well as Darboux's $27$ osculating conics.
{"title":"A recursive formula for osculating curves","authors":"G. Muratore","doi":"10.1307/mmj/20216025","DOIUrl":"https://doi.org/10.1307/mmj/20216025","url":null,"abstract":"Let $X$ be a smooth complex projective variety. Using a construction devised to Gathmann, we present a recursive formula for some of the Gromov-Witten invariants of $X$. We prove that, when $X$ is homogeneous, this formula gives the number of osculating rational curves at a general point of a general hypersurface of $X$. This generalizes the classical well known pairs of inflexion (asymptotic) lines for surfaces in $mathbb{P}^{3}$ of Salmon, as well as Darboux's $27$ osculating conics.","PeriodicalId":55569,"journal":{"name":"Arkiv for Matematik","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2020-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66232925","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}
Pub Date : 2020-02-23DOI: 10.4310/arkiv.2021.v59.n2.a6
M. Lanini, K. Zainoulline
In the present paper we extend the Riemann-Roch formalism to structure algebras of moment graphs. We introduce and study the Chern character and pushforwards for twisted fibrations of moment graphs. We prove an analogue of the Riemann-Roch theorem for moment graphs. As an application, we obtain the Riemann-Roch type theorem for equivariant $K$-theory of some Kac-Moody flag varieties.
{"title":"A Riemann–Roch type theorem for twisted fibrations of moment graphs","authors":"M. Lanini, K. Zainoulline","doi":"10.4310/arkiv.2021.v59.n2.a6","DOIUrl":"https://doi.org/10.4310/arkiv.2021.v59.n2.a6","url":null,"abstract":"In the present paper we extend the Riemann-Roch formalism to structure algebras of moment graphs. We introduce and study the Chern character and pushforwards for twisted fibrations of moment graphs. We prove an analogue of the Riemann-Roch theorem for moment graphs. As an application, we obtain the Riemann-Roch type theorem for equivariant $K$-theory of some Kac-Moody flag varieties.","PeriodicalId":55569,"journal":{"name":"Arkiv for Matematik","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2020-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48775423","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}
Pub Date : 2020-01-01DOI: 10.4310/arkiv.2020.v58.n1.a6
Nan Gao, Wencheng Zhao
We obtain new classes of singular equivalences which are constructed from Gorenstein-projective modules.
我们得到了由gorenstein -射影模构造的奇异等价的新类。
{"title":"Singular equivalences arising from Morita rings","authors":"Nan Gao, Wencheng Zhao","doi":"10.4310/arkiv.2020.v58.n1.a6","DOIUrl":"https://doi.org/10.4310/arkiv.2020.v58.n1.a6","url":null,"abstract":"We obtain new classes of singular equivalences which are constructed from Gorenstein-projective modules.","PeriodicalId":55569,"journal":{"name":"Arkiv for Matematik","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70393884","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}
Pub Date : 2020-01-01DOI: 10.4310/arkiv.2020.v58.n2.a9
Sze-Man Ngai, Yuanyuan Xie
For the class of graph-directed self-similar measures on R, which could have overlaps but are essentially of finite type, we set up a framework for deriving a closed formula for the spectral dimension of the Laplacians defined by these measures. For the class of finitely ramified graph-directed self-similar sets, the spectral dimension of the associated Laplace operators has been obtained by Hambly and Nyberg [6]. The main novelty of our results is that the graphdirected self-similar measures we consider do not need to satisfy the graph open set condition.
{"title":"Spectral asymptotics of Laplacians related to one-dimensional graph-directed self-similar measures with overlaps","authors":"Sze-Man Ngai, Yuanyuan Xie","doi":"10.4310/arkiv.2020.v58.n2.a9","DOIUrl":"https://doi.org/10.4310/arkiv.2020.v58.n2.a9","url":null,"abstract":"For the class of graph-directed self-similar measures on R, which could have overlaps but are essentially of finite type, we set up a framework for deriving a closed formula for the spectral dimension of the Laplacians defined by these measures. For the class of finitely ramified graph-directed self-similar sets, the spectral dimension of the associated Laplace operators has been obtained by Hambly and Nyberg [6]. The main novelty of our results is that the graphdirected self-similar measures we consider do not need to satisfy the graph open set condition.","PeriodicalId":55569,"journal":{"name":"Arkiv for Matematik","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70393610","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}
Pub Date : 2020-01-01DOI: 10.4310/arkiv.2020.v58.n1.a3
Khadija Ben Rejeb
Let G={ht | t∈R} be a continuous flow on a connected n-manifold M . The flow G is said to be strongly reversible by an involution τ if h−t=τhtτ for all t∈R, and it is said to be periodic if hs = identity for some s∈R∗. A closed subset K of M is called a global section for G if every orbit G(x) intersects K in exactly one point. In this paper, we study how the two properties “strongly reversible” and “has a global section” are related. In particular, we show that if G is periodic and strongly reversible by a reflection, then G has a global section.
{"title":"Periodic flows with global sections","authors":"Khadija Ben Rejeb","doi":"10.4310/arkiv.2020.v58.n1.a3","DOIUrl":"https://doi.org/10.4310/arkiv.2020.v58.n1.a3","url":null,"abstract":"Let G={ht | t∈R} be a continuous flow on a connected n-manifold M . The flow G is said to be strongly reversible by an involution τ if h−t=τhtτ for all t∈R, and it is said to be periodic if hs = identity for some s∈R∗. A closed subset K of M is called a global section for G if every orbit G(x) intersects K in exactly one point. In this paper, we study how the two properties “strongly reversible” and “has a global section” are related. In particular, we show that if G is periodic and strongly reversible by a reflection, then G has a global section.","PeriodicalId":55569,"journal":{"name":"Arkiv for Matematik","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70393807","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}
{"title":"A note on the Coifman–Fefferman and Fefferman–Stein inequalities","authors":"A. Lerner","doi":"10.4310/arkiv.2020.v58.n2.a7","DOIUrl":"https://doi.org/10.4310/arkiv.2020.v58.n2.a7","url":null,"abstract":"A condition on a Banach function space $X$ is given under which the Coifman-Fefferman and Fefferman-Stein inequalities on $X$ are equivalent.","PeriodicalId":55569,"journal":{"name":"Arkiv for Matematik","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2019-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70393554","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}
Pub Date : 2019-11-08DOI: 10.4310/arkiv.2022.v60.n1.a2
F. Deng, E. F. Wold
For a complex Lie group $G$ with a real form $G_0subset G$, we prove that any Hamiltionian automorphism $phi$ of a coadjoint orbit $mathcal O_0$ of $G_0$ whose connected components are simply connected, may be approximated by holomorphic $mathcal O_0$-invariant symplectic automorphism of the corresponding coadjoint orbit of $G$ in the sense of Carleman, provided that $mathcal O$ is closed. In the course of the proof, we establish the Hamiltonian density property for closed coadjoint orbits of all complex Lie groups.
{"title":"Hamiltonian Carleman approximation and the density property for coadjoint orbits","authors":"F. Deng, E. F. Wold","doi":"10.4310/arkiv.2022.v60.n1.a2","DOIUrl":"https://doi.org/10.4310/arkiv.2022.v60.n1.a2","url":null,"abstract":"For a complex Lie group $G$ with a real form $G_0subset G$, we prove that any Hamiltionian automorphism $phi$ of a coadjoint orbit $mathcal O_0$ of $G_0$ whose connected components are simply connected, may be approximated by holomorphic $mathcal O_0$-invariant symplectic automorphism of the corresponding coadjoint orbit of $G$ in the sense of Carleman, provided that $mathcal O$ is closed. In the course of the proof, we establish the Hamiltonian density property for closed coadjoint orbits of all complex Lie groups.","PeriodicalId":55569,"journal":{"name":"Arkiv for Matematik","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2019-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47178139","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}
Pub Date : 2019-10-23DOI: 10.4310/ARKIV.2022.v60.n1.a5
Niklas Lemcke
. We adapt ideas from Ekedahl [Eke84] to prove a Serre-type duality for Witt-divisorial sheaves of Q –Cartier divisors on a smooth projective variety over a perfect field of finite characteristic. We also explain its relationship to Tanaka’s vanishing theorems [Tan20].
{"title":"Duality for Witt-divisorial sheaves","authors":"Niklas Lemcke","doi":"10.4310/ARKIV.2022.v60.n1.a5","DOIUrl":"https://doi.org/10.4310/ARKIV.2022.v60.n1.a5","url":null,"abstract":". We adapt ideas from Ekedahl [Eke84] to prove a Serre-type duality for Witt-divisorial sheaves of Q –Cartier divisors on a smooth projective variety over a perfect field of finite characteristic. We also explain its relationship to Tanaka’s vanishing theorems [Tan20].","PeriodicalId":55569,"journal":{"name":"Arkiv for Matematik","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2019-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48200009","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}
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