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Interpolation of Closed Ideals of Bilinear Operators 双线性算子的闭理想插值
IF 0.8 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2025-01-01 DOI: 10.1007/s10114-025-3506-x
Fernando Cobos, Luz M. Fernández-Cabrera, Antón Martínez
{"title":"Interpolation of Closed Ideals of Bilinear Operators","authors":"Fernando Cobos,&nbsp;Luz M. Fernández-Cabrera,&nbsp;Antón Martínez","doi":"10.1007/s10114-025-3506-x","DOIUrl":"10.1007/s10114-025-3506-x","url":null,"abstract":"<div><p>We extend the (outer) measure <span>(gamma_{cal{I}})</span> associated to an operator ideal <span>(cal{I})</span> to a measure <span>(gamma_{frak{J}})</span> for bounded bilinear operators. If <span>(cal{I})</span> is surjective and closed, and <span>(frak{J})</span> is the class of those bilinear operators such that <span>(gamma_{frak{J}}(T)=0)</span>, we prove that <span>(frak{J})</span> coincides with the composition bideal <span>(cal{I}circfrak{B})</span>. If <span>(cal{I})</span> satisfies the Σ<sub><i>r</i></sub>-condition, we establish a simple necessary and sufficient condition for an interpolated operator by the real method to belong to <span>(frak{J})</span>. Furthermore, if in addition <span>(cal{I})</span> is symmetric, we prove a formula for the measure <span>(gamma_{frak{J}})</span> of an operator interpolated by the real method. In particular, results apply to weakly compact operators.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"41 1","pages":"209 - 230"},"PeriodicalIF":0.8,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143108139","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Weighted Maximal L2 Estimate of Operator-valued Bochner–Riesz Means 算子值Bochner-Riesz均值的加权极大L2估计
IF 0.8 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2025-01-01 DOI: 10.1007/s10114-025-3315-2
Guixiang Hong, Liyuan Zhang
{"title":"A Weighted Maximal L2 Estimate of Operator-valued Bochner–Riesz Means","authors":"Guixiang Hong,&nbsp;Liyuan Zhang","doi":"10.1007/s10114-025-3315-2","DOIUrl":"10.1007/s10114-025-3315-2","url":null,"abstract":"<div><p>In this paper, we establish a weighted maximal <i>L</i><sub>2</sub> estimate of operator-valued Bochner–Riesz means. The proof is based on noncommutative square function estimates and a sharp weighted noncommutative Hardy–Littlewood maximal inequality.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"41 1","pages":"78 - 98"},"PeriodicalIF":0.8,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143108138","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Competing Potentials Effect on Positive Solutions to a Schrödinger-Poisson System 竞争电位对Schrödinger-Poisson系统正解的影响
IF 0.8 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2024-12-26 DOI: 10.1007/s10114-024-3124-z
Haining Fan, Xiaochun Liu
{"title":"Competing Potentials Effect on Positive Solutions to a Schrödinger-Poisson System","authors":"Haining Fan,&nbsp;Xiaochun Liu","doi":"10.1007/s10114-024-3124-z","DOIUrl":"10.1007/s10114-024-3124-z","url":null,"abstract":"<div><p>In this paper, we study the multiplicity and concentration of positive solutions for a Schrödinger-Poisson system involving sign-changing potential and the nonlinearity <i>K</i>(<i>x</i>)∣<i>u</i>∣<sup><i>p</i>−2</sup><i>u</i> (2 &lt; <i>p</i> &lt; 4) in ℝ<sup>3</sup>. Such a problem cannot be studied by variational methods in a standard way, even by restricting its corresponding energy functional on the Nehari manifold since its (PS) sequence may not be bounded. By some new analytic techniques and the Ljusternik-Schnirelmann category theory, we relate the concentration and the number of positive solutions to the category of the global minima set of a suitable ground energy function. Furthermore, we investigate the asymptotic behavior of the solutions. In particular, we do not use Pohozaev equality in this work.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"41 4","pages":"1055 - 1090"},"PeriodicalIF":0.8,"publicationDate":"2024-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143908896","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Bi-predual Spaces of Generalized Campanato Spaces with Variable Growth Condition 变生长条件广义Campanato空间的双前偶空间
IF 0.8 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2024-12-20 DOI: 10.1007/s10114-024-3368-7
Satoshi Yamaguchi, Eiichi Nakai, Katsunori Shimomura
{"title":"Bi-predual Spaces of Generalized Campanato Spaces with Variable Growth Condition","authors":"Satoshi Yamaguchi,&nbsp;Eiichi Nakai,&nbsp;Katsunori Shimomura","doi":"10.1007/s10114-024-3368-7","DOIUrl":"10.1007/s10114-024-3368-7","url":null,"abstract":"<div><p>In this paper we extend the duality <span>(({overline{C_{rm comp}^{infty}({mathbb R}^{d})}}^{{rm BMO}({mathbb R}^{d})})^{ast}=H^{1}({mathbb {R}^{d}}))</span> to generalized Campanato spaces with variable growth condition <span>({cal L}_{p,phi}({mathbb R}^{d}))</span> instead of BMO(ℝ<sup><i>d</i></sup>). We also extend the characterization of <span>({overline{C_{rm comp}^{infty}({mathbb R}^{d})}}^{{rm BMO}({mathbb R}^{d})})</span> by Uchiyama (1978) to <span>({overline{C_{rm comp}^{infty}({mathbb R}^{d})}}^{{cal L}_{p,phi}({mathbb R}^{d})})</span>. Moreover, using this characterization, we prove the boundedness of singular and fractional integral operators on <span>({overline{C_{rm comp}^{infty}({mathbb R}^{d})}}^{{cal L}_{p,phi}({mathbb R}^{d})})</span>. The function space <span>({cal L}_{p,phi}({mathbb R}^{d}))</span> treated in this paper covers the case that it is coincide with Lip<sub><i>α</i></sub> on one area, with BMO on another area and with the Morrey space on the other area, for example.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"41 1","pages":"273 - 303"},"PeriodicalIF":0.8,"publicationDate":"2024-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143108781","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Boson-fermion Realization of Highest Weight Modules over (mathfrak{g}widetilde{mathfrak{l}_{M/N}}(theta)) 最高权模的一种玻色子-费米子实现 (mathfrak{g}widetilde{mathfrak{l}_{M/N}}(theta))
IF 0.8 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2024-12-15 DOI: 10.1007/s10114-024-3583-2
Fu Lin Chen, Xin Huang, Shao Bin Tan
{"title":"A Boson-fermion Realization of Highest Weight Modules over (mathfrak{g}widetilde{mathfrak{l}_{M/N}}(theta))","authors":"Fu Lin Chen,&nbsp;Xin Huang,&nbsp;Shao Bin Tan","doi":"10.1007/s10114-024-3583-2","DOIUrl":"10.1007/s10114-024-3583-2","url":null,"abstract":"<div><p>In this paper, we construct a superfermionic representation as well as a vertex representation for twisted general linear affine Lie superalgebras. We also establish a module isomorphism between them, which generalizes the super boson-fermion correspondence of type <i>B</i> given by Kac-van de Leur. Based on this isomorphism, we determine explicitly the irreducible components of these two representations. Particularly, we obtain in this way two kinds of systematic construction of level 1 irreducible integrable highest weight modules for twisted general linear affine Lie superalgebras.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"40 12","pages":"2879 - 2903"},"PeriodicalIF":0.8,"publicationDate":"2024-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142870350","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The Life Span of Classical Solutions to Nonlinear Wave Equations with Weighted Terms in Three Space Dimensions 三维带加权项非线性波动方程经典解的寿命
IF 0.8 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2024-12-15 DOI: 10.1007/s10114-024-2600-9
Hu Sheng Wang, Fan Lü
{"title":"The Life Span of Classical Solutions to Nonlinear Wave Equations with Weighted Terms in Three Space Dimensions","authors":"Hu Sheng Wang,&nbsp;Fan Lü","doi":"10.1007/s10114-024-2600-9","DOIUrl":"10.1007/s10114-024-2600-9","url":null,"abstract":"<div><p>The paper considers the Cauchy problem with small initial values for semilinear wave equations with weighted nonlinear terms. Similar to Strauss exponent <i>p</i><sub>0</sub>(<i>n</i>) which is the positive root of the quadratic equation <span>(1+{1over 2}(n+1)p-{1over 2}(n-1)p^{2}=0)</span>, we get smaller critical exponents <i>p</i><sub><i>m</i></sub>(<i>n</i>),<i>p</i><span>\u0000 <sup>*</sup><sub><i>m</i></sub>\u0000 \u0000 </span>(<i>n</i>) and have global existence in time when <i>p</i>&gt;<i>p</i><sub><i>m</i></sub>(<i>n</i>) or <i>p</i>&gt;<i>p</i><span>\u0000 <sup>*</sup><sub><i>m</i></sub>\u0000 \u0000 </span>(<i>n</i>). In addition, for the blow-up case, the introduction of the spacial weight shows the optimality of new upper and lower bound.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"40 12","pages":"2984 - 3002"},"PeriodicalIF":0.8,"publicationDate":"2024-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142870383","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Class of Robust Independence Tests Based on Weighted Integrals of Empirical Characteristic Functions 一类基于经验特征函数加权积分的鲁棒独立性检验
IF 0.8 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2024-12-15 DOI: 10.1007/s10114-024-2613-4
Feng Zou, Chang Liang Zou, Heng Jian Cui
{"title":"A Class of Robust Independence Tests Based on Weighted Integrals of Empirical Characteristic Functions","authors":"Feng Zou,&nbsp;Chang Liang Zou,&nbsp;Heng Jian Cui","doi":"10.1007/s10114-024-2613-4","DOIUrl":"10.1007/s10114-024-2613-4","url":null,"abstract":"<div><p>In this paper, we propose a class of robust independence tests for two random vectors based on weighted integrals of empirical characteristic functions. By letting weight functions be probability density functions of a class of special distributions, the proposed test statistics have simple closed forms and do not require moment conditions on the random vectors. Moreover, we derive the asymptotic distributions of the test statistics under the null hypothesis. The proposed testing method is computationally feasible and easy to implement. Based on a data-driven bandwidth selection method, Monte Carlo simulation studies indicate that our tests have a relatively good performance compared with the competitors. A real data example is also presented to illustrate the application of our tests.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"40 12","pages":"2921 - 2952"},"PeriodicalIF":0.8,"publicationDate":"2024-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142870381","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On Closed Six-Manifolds Admitting Riemannian Metrics with Positive Sectional Curvature and Non-Abelian Symmetry 具有正截面曲率和非阿贝尔对称的黎曼度量的闭六流形
IF 0.8 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2024-12-15 DOI: 10.1007/s10114-024-1418-9
Yu Hang Liu
{"title":"On Closed Six-Manifolds Admitting Riemannian Metrics with Positive Sectional Curvature and Non-Abelian Symmetry","authors":"Yu Hang Liu","doi":"10.1007/s10114-024-1418-9","DOIUrl":"10.1007/s10114-024-1418-9","url":null,"abstract":"<div><p>We study the topology of closed, simply-connected, 6-dimensional Riemannian manifolds of positive sectional curvature which admit isometric actions by SU(2) or SO(3). We show that their Euler characteristic agrees with that of the known examples, i.e., <i>S</i><sup>6</sup>, <span>(mathbb{CP}^{3})</span>, the Wallach space SU(3)/<i>T</i><sup>2</sup> and the biquotient SU(3)//<i>T</i><sup>2</sup>. We also classify, up to equivariant diffeomorphism, certain actions without exceptional orbits and show that there are strong restrictions on the exceptional strata.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"40 12","pages":"3003 - 3026"},"PeriodicalIF":0.8,"publicationDate":"2024-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142870384","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Neighbor Product Distinguishing Total Coloring of Planar Graphs without 5-cycles 无5环平面图的邻积区分全着色
IF 0.8 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2024-12-15 DOI: 10.1007/s10114-024-2622-3
Meng Ying Shi, Li Zhang
{"title":"Neighbor Product Distinguishing Total Coloring of Planar Graphs without 5-cycles","authors":"Meng Ying Shi,&nbsp;Li Zhang","doi":"10.1007/s10114-024-2622-3","DOIUrl":"10.1007/s10114-024-2622-3","url":null,"abstract":"<div><p>Given a simple graph <i>G</i> and a proper total-<i>k</i>-coloring <i>φ</i> from <i>V</i> (<i>G</i>) ∪ <i>E(G)</i> to {<i>1, 2</i>,…,<i>k</i>}. Let <i>f</i>(<i>v</i>) = <i>φ</i>(<i>v</i>)Π<sub><i>uv</i>∈<i>E(G)</i></sub><i>φ</i>(<i>uv</i>). The coloring <i>φ</i> is neighbor product distinguishing if <i>f</i>(<i>u</i>) ≠ <i>f</i>(<i>v</i>) for each edge <i>uv</i> ∈ <i>E</i>(<i>G</i>). The neighbor product distinguishing total chromatic number of <i>G</i>, denoted by <span>(chi_{Pi}^{primeprime}(G))</span>, is the smallest integer <i>k</i> such that <i>G</i> admits a <i>k</i>-neighbor product distinguishing total coloring. Li et al. conjectured that <span>(chi_{Pi}^{primeprime}(G)leq Delta(G)+3)</span> for any graph with at least two vertices. Dong et al. showed that conjecture holds for planar graphs with maximum degree at least 10. By using the famous Combinatorial Nullstellensatz, we prove that if <i>G</i> is a planar graph without 5-cycles, then <span>(chi_{Pi}^{primeprime}(G)leq max{Delta(G)+2,12})</span>.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"40 12","pages":"2904 - 2920"},"PeriodicalIF":0.8,"publicationDate":"2024-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142870386","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Asymptotic Independence of the Quadratic Form and Maximum of Independent Random Variables with Applications to High-Dimensional Tests 二次型的渐近独立性和独立随机变量的极大值及其在高维检验中的应用
IF 0.8 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2024-12-15 DOI: 10.1007/s10114-024-2498-2
Da Chuan Chen, Long Feng, De Cai Liang
{"title":"Asymptotic Independence of the Quadratic Form and Maximum of Independent Random Variables with Applications to High-Dimensional Tests","authors":"Da Chuan Chen,&nbsp;Long Feng,&nbsp;De Cai Liang","doi":"10.1007/s10114-024-2498-2","DOIUrl":"10.1007/s10114-024-2498-2","url":null,"abstract":"<div><p>This paper establishes the asymptotic independence between the quadratic form and maximum of a sequence of independent random variables. Based on this theoretical result, we find the asymptotic joint distribution for the quadratic form and maximum, which can be applied into the high-dimensional testing problems. By combining the sum-type test and the max-type test, we propose the Fisher’s combination tests for the one-sample mean test and two-sample mean test. Under this novel general framework, several strong assumptions in existing literature have been relaxed. Monte Carlo simulation has been done which shows that our proposed tests are strongly robust to both sparse and dense data.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"40 12","pages":"3093 - 3126"},"PeriodicalIF":0.8,"publicationDate":"2024-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142870389","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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