Acta Mathematica Sinica-English Series最新文献

{"title":"Different Hearts on Elliptic Curves","authors":"Yucheng Liu","doi":"10.1007/s10114-025-3286-3","DOIUrl":"10.1007/s10114-025-3286-3","url":null,"abstract":"<div><p>The classical Mumford stability condition of vector bundles on a complex elliptic curve <i>X</i>, can be viewed as a Bridgeland stability condition on <i>D</i>^<i>b</i> (Coh <i>X</i>), the bounded derived category of coherent sheaves on <i>X</i>. This point of view gives us infinitely many <i>t</i>-structures and hearts on <i>D</i>^<i>b</i> (Coh <i>X</i>). In this paper, we answer the question which of these hearts are Noetherian or Artinian.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"41 3","pages":"847 - 853"},"PeriodicalIF":0.8,"publicationDate":"2025-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143688519","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}

{"title":"Additively Indecomposable Positive Definite Integral Lattices","authors":"Ruiqing Wang","doi":"10.1007/s10114-025-2562-6","DOIUrl":"10.1007/s10114-025-2562-6","url":null,"abstract":"<div><p>In this paper, we obtain some sufficient and necessary conditions for indecomposable positive definite integral lattices with discriminants 2, 3, 4 and 5 over <span>({mathbb Z})</span> being additively indecomposable lattices. Using these results, we prove that there exist additively indecomposable positive integral quadratic lattices with discriminants 2, 3, 4 and 5 and rank greater than or equal to 2 but for 35 exceptions. In the exceptions there are no lattices with the desired properties. We also give a lifting theorem of additively indecomposable positive definite integral lattices.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"41 3","pages":"908 - 924"},"PeriodicalIF":0.8,"publicationDate":"2025-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143688520","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}

{"title":"Cotorsion Pairs on m-term Subcategories","authors":"Yu Liu,&nbsp;Panyue Zhou","doi":"10.1007/s10114-025-2286-7","DOIUrl":"10.1007/s10114-025-2286-7","url":null,"abstract":"<div><p>Let <span>({cal C})</span> be a triangulated category. We define <i>m</i>-term subcategories on <span>({cal C})</span> induced by <i>n</i>-rigid subcategories, which are extriangulated subcategories of <span>({cal C})</span>. Then we give a one-to-one correspondence between cotorsion pairs on 2-term subcategories <span>({cal G})</span> and support <i>τ</i>-tilting subcategories on an abelian quotient of <span>({cal G})</span>. If an <i>m</i>-term subcategory is induced by a co-t-structure, then we have a one-to-one correspondence between cotorsion pairs on it and cotorsion pairs on <span>({cal C})</span> under certain conditions.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"41 3","pages":"1023 - 1036"},"PeriodicalIF":0.8,"publicationDate":"2025-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143688563","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}

{"title":"Jump and Variational Inequalities for Singular Integral with Rough Kernel","authors":"Yanping Chen,&nbsp;Liu Yang,&nbsp;Meng Qu","doi":"10.1007/s10114-025-3462-5","DOIUrl":"10.1007/s10114-025-3462-5","url":null,"abstract":"<div><p>In this paper, we consider the jump and variational inequalities of truncated singular integral operator with rough kernel</p><div><div><span>$$T_{Omega,beta,varepsilon}f(x)=int_{mid ymid&gt;varepsilon}{Omega(y)over mid ymid ^{n-beta}}f(x-y)dy,$$</span></div></div><p>where the kernel <span>(Omega in (L(log^{+}L)^{2})^{n over{n-beta}}(mathbb{S}^{n-1}))</span> satisfies the vanishing condition and the homogeneous condition of degree 0. This kind of singular integral appears in the approximation of the surface quasi-geostrophic (SQG) equation from the generalized SQG equation. We establish the (<i>L</i>^<i>p</i>, <i>L</i>^<i>q</i>) estimate of the jump and variational inequalities of the families {<i>T</i>_{<i>Ω,β,ε</i>}}_{<i>ε</i>&gt;0} for <span>({1over q}={1over p}-{betaover n})</span> and 0 &lt; <i>β</i> &lt; 1. Moreover, one can get the <i>L</i>^<i>p</i> boundedness of the Calderón–Zygmund operator with the same kernel by letting <i>β</i> → 0⁺.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"41 1","pages":"149 - 168"},"PeriodicalIF":0.8,"publicationDate":"2025-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143108864","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}

{"title":"Restricting Riesz–Logarithmic-Gagliardo–Lipschitz Potentials","authors":"Xinting Hu,&nbsp;Liguang Liu","doi":"10.1007/s10114-025-3458-1","DOIUrl":"10.1007/s10114-025-3458-1","url":null,"abstract":"<div><p>For <i>s</i> ∈ [0, 1], <i>b</i> ∈ ℝ and <i>p</i> ∈ [1, ∞), let <span>(dot{B}_{p,infty}^{s,b}(mathbb{R}^{n}))</span> be the logarithmic-Gagliardo–Lipschitz space, which arises as a limiting interpolation space and coincides to the classical Besov space when <i>b</i> = 0 and <i>s</i> ∈ (0, 1). In this paper, the authors study restricting principles of the Riesz potential space <span>(cal{I}_{alpha}(dot{B}_{p,infty}^{s,b}(mathbb{R}^{n})))</span> into certain Radon–Campanato space.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"41 1","pages":"131 - 148"},"PeriodicalIF":0.8,"publicationDate":"2025-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143108452","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}

{"title":"A Quantitative Second Order Sobolev Regularity for (inhomogeneous) Normalized p(·)-Laplace Equations","authors":"Yuqing Wang,&nbsp;Yuan Zhou","doi":"10.1007/s10114-025-3356-6","DOIUrl":"10.1007/s10114-025-3356-6","url":null,"abstract":"<div><p>Let Ω be a domain of ℝ^<i>n</i> with <i>n</i> ≥ 2 and <i>p</i>(·) be a local Lipschitz funcion in Ω with 1 &lt; <i>p</i>(<i>x</i>) &lt; ∞ in Ω. We build up an interior quantitative second order Sobolev regularity for the normalized <i>p</i>(·)-Laplace equation −Δ<span>\u0000 ^<i>N</i>_<i>p</i>(·)\u0000 \u0000 </span><i>u</i> = 0 in Ω as well as the corresponding inhomogeneous equation −Δ<span>\u0000 ^<i>N</i>_<i>p</i>(·)\u0000 \u0000 </span><i>u</i> =<i>f</i> in Ω with <i>f</i> ∈ <i>C</i>⁰(Ω). In particular, given any viscosity solution <i>u</i> to −Δ<span>\u0000 ^<i>N</i>_<i>p</i>(·)\u0000 \u0000 </span><i>u</i> = 0 in Ω, we prove the following:\u0000</p><ol>\u0000 <li>\u0000 <span>(i)</span>\u0000 \u0000 <p>in dimension <i>n</i> = 2, for any subdomain <i>U</i> ⋐ Ω and any <i>β</i> ≥ 0, one has ∣<i>Du</i>∣^<i>β</i><i>Du</i> ∈ <i>L</i><span>\u0000 ^2+<i>δ</i>_loc\u0000 \u0000 </span> (<i>U</i>) with a quantitative upper bound, and moreover, the map <span>((x_{1},x_{2})rightarrowvert Duvert^{beta}(u_{x_{1}},-u_{x_{2}}))</span> is quasiregular in <i>U</i> in the sense that </p><div><div><span>$$vert D[vert Duvert^{beta};Du]vert^{2}leq-C;text{det};D[vert Duvert^{beta};Du];;;;;text{a.e.};text{in};U.$$</span></div></div>\u0000 \u0000 </li>\u0000 <li>\u0000 <span>(ii)</span>\u0000 \u0000 <p>in dimension <i>n</i> ≥ 3, for any subdomain <i>U</i> ⋐ Ω with inf_<i>U</i> <i>p</i>(<i>x</i>) &gt; 1 and <span>(text{sup}_{U};p(x)&lt;3+{2over{n-2}})</span>, one has <i>D</i>²<i>u</i> ∈ <i>L</i><span>\u0000 ^2+<i>δ</i>_loc\u0000 \u0000 </span> (<i>U</i>) with a quantitative upper bound, and also with a pointwise upper bound </p><div><div><span>$$vert D^{2}uvert^{2}leq-Csum_{1leq i&lt;jleq n}[u_{x_{i}x_{j}}u_{x_{j}x_{i}}-u_{x_{i}x_{i}}u_{x_{j}x_{j}}];;;;;text{a.e};text{in};U.$$</span></div></div>\u0000 \u0000 </li>\u0000 </ol><p>Here constants <i>δ</i> &gt; 0 and <i>C</i> ≥ 1 are independent of <i>u</i>. These extend the related results obtaind by Adamowicz–Hästö [Mappings of finite distortion and PDE with nonstandard growth. <i>Int. Math. Res. Not. IMRN</i>, <b>10</b>, 1940–1965 (2010)] when <i>n</i> = 2 and <i>β</i> = 0.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"41 1","pages":"99 - 121"},"PeriodicalIF":0.8,"publicationDate":"2025-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143108455","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}

{"title":"Remarks on Almost Everywhere Convergence and Approximate Identities","authors":"Sean Douglas,&nbsp;Loukas Grafakos","doi":"10.1007/s10114-025-3557-z","DOIUrl":"10.1007/s10114-025-3557-z","url":null,"abstract":"<div><p>We prove almost everywhere convergence for convolutions of locally integrable functions with shrinking <i>L</i>¹ dilations of a fixed integrable kernel with an integrable radially decreasing majorant. The set on which the convergence holds is an explicit subset of the Lebesgue set of the locally integrable function of full measure. This result can be viewed as an extension of the Lebesgue differentiation theorem in which the characteristic function of the unit ball is replaced by a more general kernel. We obtain a similar result for multilinear convolutions.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"41 1","pages":"255 - 272"},"PeriodicalIF":0.8,"publicationDate":"2025-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143108857","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}

{"title":"On Weighted Compactness of Commutators of Bilinear Vector-valued Singular Integral Operators and Applications","authors":"Zhengyang Li,&nbsp;Liu Lu,&nbsp;Fanghui Liao,&nbsp;Qingying Xue","doi":"10.1007/s10114-025-3465-2","DOIUrl":"10.1007/s10114-025-3465-2","url":null,"abstract":"<div><p>Let <i>T</i> be a bilinear vector-valued singular integral operator satisfies some mild regularity conditions, which may not fall under the scope of the theory of standard Calderón–Zygmund classes. For any <span>(vec{b}=(b_{1},b_{2})in (text{CMO}(mathbb{R}^{n}))^{2})</span>, let <span>([T,b_{j}]_{e_{j}} (j=1,2), [T,vec{b}]_{alpha})</span> be the commutators in the <i>j</i>-th entry and the iterated commutators of <i>T</i>, respectively. In this paper, for all <i>p</i>₀ &gt; 1, <span>({p_{0}over 2} &lt; p &lt; infty)</span>, and <i>p</i>₀ ≤ <i>p</i>₁, <i>p</i>₂ &lt; ∞ with 1/<i>p</i> = 1/<i>p</i>₁ + 1/<i>p</i>₂, we prove that <span>([T,b_{j}]_{e_{j}})</span> and <span>([T,vec{b}]_{alpha})</span> are weighted compact operators from <span>(L^{p_{1}}(w_{1})times L^{p_{2}}(w_{2}))</span> to <span>(L^{p}(nu_{vec{w}}))</span>, where <span>(vec{w}=(w_{1},w_{2})in A_{vec{p}/p_{0}})</span> and <span>(nu_{vec{w}}=w_{1}^{p/p_{1}}w_{2}^{p/p_{2}})</span>. As applications, we obtain the weighted compactness of commutators in the <i>j</i>-th entry and the iterated commutators of several kinds of bilinear Littlewood–Paley square operators with some mild kernel regularity, including bilinear <i>g</i> function, bilinear <i>g</i>*_<i>λ</i> function and bilinear Lusin’s area integral. In addition, we also get the weighted compactness of commutators in the <i>j</i>-th entry and the iterated commutators of bilinear Fourier multiplier operators, and bilinear square Fourier multiplier operators associated with bilinear <i>g</i> function, bilinear <i>g</i>*_<i>λ</i> function and bilinear Lusin’s area integral, respectively.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"41 1","pages":"169 - 190"},"PeriodicalIF":0.8,"publicationDate":"2025-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143108465","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}

{"title":"Wavelet Characterizations of Variable Anisotropic Hardy Spaces","authors":"Yao He,&nbsp;Yong Jiao,&nbsp;Jun Liu","doi":"10.1007/s10114-025-3567-x","DOIUrl":"10.1007/s10114-025-3567-x","url":null,"abstract":"<div><p>Let <i>p</i>(·): ℝ^<i>n</i> → (0, ∞] be a variable exponent function satisfying the globally log-Hölder continuous condition and <i>A</i> a general expansive matrix on ℝ^<i>n</i>. Let H<span>\u0000 ^<i>p</i>(·)_<i>A</i>\u0000 \u0000 </span>(ℝ^<i>n</i>) be the variable anisotropic Hardy space associated with <i>A</i>. In this paper, via first establishing a criterion for affirming some functions being in the space <i>H</i><span>\u0000 ^<i>p</i>(·)_<i>A</i>\u0000 \u0000 </span>(ℝ^<i>n</i>), the authors obtain several equivalent characterizations of <i>H</i><span>\u0000 ^<i>p</i>(·)_<i>A</i>\u0000 \u0000 </span>(ℝ^<i>n</i>) in terms of the so-called tight frame multiwavelets, which extend the well-known wavelet characterizations of classical Hardy spaces. In particular, these wavelet characterizations are shown without the help of Peetre maximal operators.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"41 1","pages":"304 - 326"},"PeriodicalIF":0.8,"publicationDate":"2025-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143108858","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}

{"title":"Musielak–Orlicz–Lorentz Hardy Spaces: Maximal Function, Finite Atomic, and Littlewood–Paley Characterizations with Applications to Dual Spaces and Summability of Fourier Transforms","authors":"Hongchao Jia,&nbsp;Der-Chen Chang,&nbsp;Ferenc Weisz,&nbsp;Dachun Yang,&nbsp;Wen Yuan","doi":"10.1007/s10114-025-3153-2","DOIUrl":"10.1007/s10114-025-3153-2","url":null,"abstract":"<div><p>Let <i>q</i> ∈ (0, ∞] and <i>φ</i> be a Musielak–Orlicz function with uniformly lower type <i>p</i><span>\u0000 ⁻_<i>φ</i>\u0000 \u0000 </span> ∈ (0, ∞) and uniformly upper type <i>p</i><span>\u0000 ⁺_<i>φ</i>\u0000 \u0000 </span> ∈ (0, ∞). In this article, the authors establish various real-variable characterizations of the Musielak–Orlicz–Lorentz Hardy space <i>H</i>^<i>φ,q</i>(ℝ^<i>n</i>), respectively, in terms of various maximal functions, finite atoms, and various Littlewood–Paley functions. As applications, the authors obtain the dual space of <i>H</i>^<i>φ,q</i>(ℝ^<i>n</i>) and the summability of Fourier transforms from <i>H</i>^<i>φ,q</i>(ℝ^<i>n</i>) to the Musielak–Orlicz–Lorentz space <i>L</i>^<i>φ,q</i>(ℝ^<i>n</i>) when <i>q</i> ∈ (0, ∞) or from the Musielak–Orlicz Hardy space <i>H</i>^<i>φ</i>(ℝ^<i>n</i>) to <i>L</i>^<i>φ,q</i>(ℝ^<i>n</i>) in the critical case. These results are new when <i>q</i> ∈ (0, ∞) and also essentially improve the existing corresponding results (if any) in the case <i>q</i> = ∞ via removing the original assumption that <i>φ</i> is concave. To overcome the essential obstacles caused by both that <i>φ</i> may not be concave and that the boundedness of the powered Hardy–Littlewood maximal operator on associated spaces of Musielak–Orlicz spaces is still unknown, the authors make full use of the obtained atomic characterization of <i>H</i>^<i>φ,q</i>(ℝ^<i>n</i>), the corresponding results related to weighted Lebesgue spaces, and the subtle relation between Musielak–Orlicz spaces and weighted Lebesgue spaces.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"41 1","pages":"1 - 77"},"PeriodicalIF":0.8,"publicationDate":"2025-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143108863","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}