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Boundedness estimate for certain Calderón–Zygmund type singular integrals on (textrm{BMO}) spaces (textrm{BMO})空间上某些Calderón-Zygmund型奇异积分的有界性估计
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-04-29 DOI: 10.1007/s00013-025-02119-9
Yinping Xin, Sibei Yang
{"title":"Boundedness estimate for certain Calderón–Zygmund type singular integrals on (textrm{BMO}) spaces","authors":"Yinping Xin,&nbsp;Sibei Yang","doi":"10.1007/s00013-025-02119-9","DOIUrl":"10.1007/s00013-025-02119-9","url":null,"abstract":"<div><p>Let <span>(beta in (0,n))</span>. In this paper, we study the boundedness of the Calderón–Zygmund type singular integral </p><div><div><span>$$ T(f)(x):=mathrm {p.v.}int limits _{mathbb {R}^n}frac{Omega (y)}{|y|^{n-beta }}f(x-y),dy $$</span></div></div><p>on the space <span>(textrm{BMO}(mathbb {R}^n))</span>. Precisely, let <span>(qin (1,infty ))</span> and <span>(beta in (0,frac{(q-1)n}{q}))</span>. We prove that, for any <span>(fin textrm{BMO}(mathbb {R}^n)cap L^{q'}(mathbb {R}^n))</span>, <span>(Tfin textrm{BMO}(mathbb {R}^n))</span> and </p><div><div><span>$$ Vert TfVert _{textrm{BMO}(mathbb {R}^n)}le Cleft[ Vert fVert _{textrm{BMO}(mathbb {R}^n)}+frac{beta ^{frac{(q-1)n}{q}}}{root q of {n(q-1)-beta q}}Vert fVert _{L^{q'}(mathbb {R}^n)}right] , $$</span></div></div><p>where <span>(q'in (1,infty ))</span> is given by <span>(1/q+1/q'=1)</span> and <i>C</i> is a positive constant independent of <span>(beta )</span> and <i>f</i>. This estimate can be seen as a further development for the corresponding results in the scale of Lebesgue spaces, established by Chen and Guo (J Funct Anal 281:Paper No. 109196, 2021), in the endpoint case.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"125 1","pages":"93 - 106"},"PeriodicalIF":0.5,"publicationDate":"2025-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145171287","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}
引用次数: 0
Is there a group structure on the Galois cohomology of a reductive group over a global field? 在全局域上约化群的伽罗瓦上同调上是否存在群结构？
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-04-28 DOI: 10.1007/s00013-025-02118-w
Mikhail Borovoi
{"title":"Is there a group structure on the Galois cohomology of a reductive group over a global field?","authors":"Mikhail Borovoi","doi":"10.1007/s00013-025-02118-w","DOIUrl":"10.1007/s00013-025-02118-w","url":null,"abstract":"<div><p>Let <i>K</i> be a global field, that is, a number field or a global function field. It is known that the answer to the question in the title over <i>K</i> is “Yes” when <i>K</i> has no real embeddings. We show that otherwise the answer is “No”. Namely, we show that when <i>K</i> is a number field admitting a real embedding, it is impossible to define a group structure on the first Galois cohomology sets <span>(textrm{H}^1hspace{-0.8pt}(K,G))</span> for all reductive <i>K</i>-groups <i>G</i> in a functorial way.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"124 6","pages":"583 - 589"},"PeriodicalIF":0.5,"publicationDate":"2025-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00013-025-02118-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144085002","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the pair correlation statistic of sequences with the finite gap property 有限间隙序列的对相关统计量
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-04-25 DOI: 10.1007/s00013-025-02126-w
Jasmin Fiedler, Christian Weiss
{"title":"On the pair correlation statistic of sequences with the finite gap property","authors":"Jasmin Fiedler,&nbsp;Christian Weiss","doi":"10.1007/s00013-025-02126-w","DOIUrl":"10.1007/s00013-025-02126-w","url":null,"abstract":"<div><p>The limiting function <i>f</i>(<i>s</i>) of the pair correlation </p><div><div><span>$$begin{aligned} frac{1}{N} # left{ 1 le ine jle N bigg vert leftVert x_i - x_j rightVert le frac{s}{N} right} end{aligned}$$</span></div></div><p>for a sequence <span>((x_N)_{N in mathbb {N}})</span> on the torus <span>(mathbb {T}^1)</span> is said to be Poissonian if it exists and equals 2<i>s</i> for all <span>(s ge 0)</span>. For instance, independent, uniformly distributed random variables generically have this property. Obviously <i>f</i>(<i>s</i>) is always a monotonic function if existent. There are only few examples of sequences where <span>(f(s) ne 2s)</span>, but where the limit can still be explicitly calculated. Therefore, it is an open question which types of functions <i>f</i>(<i>s</i>) can or cannot appear here. In this note, we give a partial answer on this question by addressing the case that the number of different gap lengths in the sequence is finite and showing that <i>f</i> cannot be continuous then.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"125 1","pages":"107 - 113"},"PeriodicalIF":0.5,"publicationDate":"2025-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00013-025-02126-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145168500","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Finite groups whose subgroup graph contains a vertex of large degree 子群图包含一个大次顶点的有限群
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-04-04 DOI: 10.1007/s00013-025-02121-1
Marius Tărnăuceanu
{"title":"Finite groups whose subgroup graph contains a vertex of large degree","authors":"Marius Tărnăuceanu","doi":"10.1007/s00013-025-02121-1","DOIUrl":"10.1007/s00013-025-02121-1","url":null,"abstract":"<div><p>Burness and Scott (J Aust Math Soc 87:329-357, 2009) classified finite groups <i>G</i> such that the number of prime order subgroups of <i>G</i> is greater than <span>(|G|/2-1)</span>. In this note, we study finite groups <i>G</i> whose subgroup graph contains a vertex of degree greater than <span>(|G|/2-1)</span>. The classification given for finite solvable groups extends the work of Burness and Scott.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"124 5","pages":"475 - 484"},"PeriodicalIF":0.5,"publicationDate":"2025-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00013-025-02121-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143818135","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
MacMahonesque partition functions detect sets related to primes MacMahonesque配分函数检测与素数相关的集合
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-04-02 DOI: 10.1007/s00013-025-02109-x
Kevin Gomez
{"title":"MacMahonesque partition functions detect sets related to primes","authors":"Kevin Gomez","doi":"10.1007/s00013-025-02109-x","DOIUrl":"10.1007/s00013-025-02109-x","url":null,"abstract":"<div><p>Recent work by Craig, van Ittersum, and Ono constructs explicit expressions in the partition functions of MacMahon that detect the prime numbers. Furthermore, they define generalizations, the MacMahonesque functions, and prove there are infinitely many such expressions in these functions. Here, we show how to modify and adapt their construction to detect cubes of primes as well as primes in arithmetic progressions.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"124 6","pages":"637 - 652"},"PeriodicalIF":0.5,"publicationDate":"2025-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00013-025-02109-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144084870","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Multiplicity of powers of squarefree monomial ideals 无平方单项式理想的幂的多重性
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-03-26 DOI: 10.1007/s00013-025-02116-y
Phan Thi Thuy, Thanh Vu
{"title":"Multiplicity of powers of squarefree monomial ideals","authors":"Phan Thi Thuy,&nbsp;Thanh Vu","doi":"10.1007/s00013-025-02116-y","DOIUrl":"10.1007/s00013-025-02116-y","url":null,"abstract":"<div><p>Let <i>I</i> be an arbitrary nonzero squarefree monomial ideal of dimension <i>d</i> in a polynomial ring <span>(S = textrm{k}[x_1,ldots ,x_n])</span>. Let <span>(mu )</span> be the number of associated primes of <i>S</i>/<i>I</i> of dimension <i>d</i>. We prove that the multiplicity of powers of <i>I</i> is given by </p><div><div><span>$$begin{aligned} e_0(S/I^s) = mu left( {begin{array}{c}n-d+s-1 s-1end{array}}right) end{aligned}$$</span></div></div><p>for all <span>(s ge 1)</span>. Consequently, we compute the multiplicity of all powers of path ideals of cycles.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"125 1","pages":"9 - 15"},"PeriodicalIF":0.5,"publicationDate":"2025-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145169565","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}
引用次数: 0
Banach algebras of sequences of generalized bounded variation 广义有界变分序列的Banach代数
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-03-24 DOI: 10.1007/s00013-025-02117-x
John A. Lindberg Jr., Robert Kantrowitz
{"title":"Banach algebras of sequences of generalized bounded variation","authors":"John A. Lindberg Jr.,&nbsp;Robert Kantrowitz","doi":"10.1007/s00013-025-02117-x","DOIUrl":"10.1007/s00013-025-02117-x","url":null,"abstract":"<div><p>This article is to shed light on a class of commutative unital complex Banach algebras. We show that these Banach algebras of sequences of generalized bounded variation are all semi-simple, regular, and self-adjoint and that their carrier spaces are homeomorphic to compactifications of the discrete space of positive integers. In particular, we provide necessary and sufficient conditions under which the carrier space may be identified with the one-point compactification or the Stone–Čech compactification of the positive integers. It turns out that the carrier spaces of many of the Banach algebras under consideration are neither of these familiar compactifications.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"124 6","pages":"653 - 660"},"PeriodicalIF":0.5,"publicationDate":"2025-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144084909","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}
引用次数: 0
A character theoretic formula for the base size 基本尺寸的特征理论公式
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-03-24 DOI: 10.1007/s00013-025-02120-2
Coen del Valle
{"title":"A character theoretic formula for the base size","authors":"Coen del Valle","doi":"10.1007/s00013-025-02120-2","DOIUrl":"10.1007/s00013-025-02120-2","url":null,"abstract":"<div><p>A base for a permutation group <i>G</i> acting on a set <span>(Omega )</span> is a sequence <span>({mathcal {B}})</span> of points of <span>(Omega )</span> such that the pointwise stabiliser <span>(G_{{mathcal {B}}})</span> is trivial. The base size of <i>G</i> is the size of a smallest base for <i>G</i>. We derive a character theoretic formula for the base size of a class of groups admitting a certain kind of irreducible character. Moreover, we prove a formula for enumerating the non-equivalent bases for <i>G</i> of size <span>(lin {mathbb {N}}.)</span> As a consequence of our results, we present a very short, entirely algebraic proof of the formula of Mecenero and Spiga for the base size of the symmetric group <span>(textrm{S}_n)</span> acting on the <i>k</i>-element subsets of <span>({1,2,3,ldots ,n}.)</span> Our methods also provide a formula for the base size of many product type permutation groups.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"124 5","pages":"485 - 490"},"PeriodicalIF":0.5,"publicationDate":"2025-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00013-025-02120-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143818178","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Unmixed polymatroidal ideals 未混合的多面体理想
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-03-24 DOI: 10.1007/s00013-025-02115-z
Mozghan Koolani, Amir Mafi, Hero Saremi
{"title":"Unmixed polymatroidal ideals","authors":"Mozghan Koolani,&nbsp;Amir Mafi,&nbsp;Hero Saremi","doi":"10.1007/s00013-025-02115-z","DOIUrl":"10.1007/s00013-025-02115-z","url":null,"abstract":"<div><p>Let <span>(R=K[x_1,ldots ,x_n])</span> denote the polynomial ring in <i>n</i> variables over a field <i>K</i> and <i>I</i> be a polymatroidal ideal of <i>R</i>. In this paper, we provide a comprehensive classification of all unmixed polymatroidal ideals. This work addresses a question raised by Herzog and Hibi (Eur J Comb 27:513–517, 2006).</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"124 6","pages":"625 - 635"},"PeriodicalIF":0.5,"publicationDate":"2025-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144084908","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}
引用次数: 0
On the normal complement problem for finite group algebras of abelian-by-cyclic groups 关于阿贝尔环群有限群代数的正规补问题
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-03-23 DOI: 10.1007/s00013-025-02114-0
Allen Herman, Surinder Kaur
{"title":"On the normal complement problem for finite group algebras of abelian-by-cyclic groups","authors":"Allen Herman,&nbsp;Surinder Kaur","doi":"10.1007/s00013-025-02114-0","DOIUrl":"10.1007/s00013-025-02114-0","url":null,"abstract":"<div><p>Assume <i>F</i> is a finite field of order <span>(p^f)</span> and <i>q</i> is an odd prime for which <span>(p^f-1=sq^m)</span>, where <span>(m ge 1)</span> and <span>((s,q)=1)</span>. In this article, we obtain the order of the symmetric and the unitary subgroup of the semisimple group algebra <span>(FC_q.)</span> Further, for the extension <i>G</i> of <span>(C_q = langle b rangle )</span> by an abelian group <i>A</i> of order <span>(p^n)</span> with <span>(C_{A}(b) = {e})</span>, we prove that if <span>(m&gt;1,)</span> or <span>((s+1) ge q)</span> and <span>(2n ge f(q-1))</span>, then <i>G</i> does not have a normal complement in <i>V</i>(<i>FG</i>).</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"124 5","pages":"491 - 501"},"PeriodicalIF":0.5,"publicationDate":"2025-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143818165","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}
引用次数: 0
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