Bulletin of the London Mathematical Society最新文献_第7页

Mixed L p $L^p$ estimates for transforms of noncommutative martingales

IF 0.8 3区数学

Bulletin of the London Mathematical Society Pub Date : 2024-11-11 DOI: 10.1112/blms.13184

Adam Osękowski

{"title":"Mixed \u0000 \u0000 \u0000 L\u0000 p\u0000 \u0000 $L^p$\u0000 estimates for transforms of noncommutative martingales","authors":"Adam Osękowski","doi":"10.1112/blms.13184","DOIUrl":"https://doi.org/10.1112/blms.13184","url":null,"abstract":"Let <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mn>1</mn>\u0000 <mo><</mo>\u0000 <mi>p</mi>\u0000 <mo><</mo>\u0000 <mspace></mspace>\u0000 <mi>q</mi>\u0000 <mo><</mo>\u0000 <mi>∞</mi>\u0000 </mrow>\u0000 <annotation>$1<p<, q<infty $</annotation>\u0000 </semantics></math>. The paper is devoted to the study of <math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mi>L</mi>\u0000 <mi>q</mi>\u0000 </msup>\u0000 <mo>→</mo>\u0000 <msup>\u0000 <mi>L</mi>\u0000 <mi>p</mi>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$L^qrightarrow L^p$</annotation>\u0000 </semantics></math> estimates for transforms of noncommutative martingales, under the assumption that the transforming sequence takes values in <math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>L</mi>\u0000 <mi>r</mi>\u0000 </msup>\u0000 <annotation>$L^r$</annotation>\u0000 </semantics></math>, <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mn>1</mn>\u0000 <mo>/</mo>\u0000 <mi>r</mi>\u0000 <mo>=</mo>\u0000 <mn>1</mn>\u0000 <mo>/</mo>\u0000 <mi>p</mi>\u0000 <mo>−</mo>\u0000 <mn>1</mn>\u0000 <mo>/</mo>\u0000 <mi>q</mi>\u0000 </mrow>\u0000 <annotation>$1/r=1/p-1/q$</annotation>\u0000 </semantics></math>. This goes beyond the usual context of <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>p</mi>\u0000 <mo>=</mo>\u0000 <mi>q</mi>\u0000 </mrow>\u0000 <annotation>$p=q$</annotation>\u0000 </semantics></math> and <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>r</mi>\u0000 <mo>=</mo>\u0000 <mi>∞</mi>\u0000 </mrow>\u0000 <annotation>$r=infty$</annotation>\u0000 </semantics></math> studied so far in the literature. The obtained constants are of optimal order at the endpoints, in addition the approach allows to obtain sharp values in the range <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>p</mi>\u0000 <mo>⩽</mo>\u0000 <mn>2</mn>\u0000 <mo>⩽</mo>\u0000 <mi>q</mi>\u0000 </mrow>\u0000 <annotation>$pleqslant 2leqslant q$</annotation>\u0000 </semantics></math>. The proof rests on real interpolation-type arguments for martingale transforms, which are of independent interest.","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"57 1","pages":"96-114"},"PeriodicalIF":0.8,"publicationDate":"2024-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143114395","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

Decoupling for Schatten class operators in the setting of quantum harmonic analysis

IF 0.8 3区数学

Bulletin of the London Mathematical Society Pub Date : 2024-11-08 DOI: 10.1112/blms.13178

Helge J. Samuelsen

{"title":"Decoupling for Schatten class operators in the setting of quantum harmonic analysis","authors":"Helge J. Samuelsen","doi":"10.1112/blms.13178","DOIUrl":"https://doi.org/10.1112/blms.13178","url":null,"abstract":"We introduce the notion of decoupling for operators, and prove an equivalence between classical <math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mi>ℓ</mi>\u0000 <mi>q</mi>\u0000 </msup>\u0000 <msup>\u0000 <mi>L</mi>\u0000 <mi>p</mi>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$ell ^qL^p$</annotation>\u0000 </semantics></math> decoupling for functions and <math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mi>ℓ</mi>\u0000 <mi>q</mi>\u0000 </msup>\u0000 <msup>\u0000 <mi>S</mi>\u0000 <mi>p</mi>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$ell ^q{mathcal {S}}^p$</annotation>\u0000 </semantics></math> decoupling for operators on bounded sets in <math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>R</mi>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 <mi>d</mi>\u0000 </mrow>\u0000 </msup>\u0000 <annotation>${mathbb {R}}^{2d}$</annotation>\u0000 </semantics></math>. We also show that the equivalence depends only on the bounded set <math>\u0000 <semantics>\u0000 <mi>Ω</mi>\u0000 <annotation>$Omega$</annotation>\u0000 </semantics></math> and not on the values of <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>p</mi>\u0000 <mo>,</mo>\u0000 <mi>q</mi>\u0000 </mrow>\u0000 <annotation>$p,q$</annotation>\u0000 </semantics></math> nor on the partition of <math>\u0000 <semantics>\u0000 <mi>Ω</mi>\u0000 <annotation>$Omega$</annotation>\u0000 </semantics></math>. The proof relies on a quantum version of Wiener's division lemma.","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"57 1","pages":"23-37"},"PeriodicalIF":0.8,"publicationDate":"2024-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/blms.13178","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143113568","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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

Infinite unrestricted sumsets of the form B + B $B+B$ in sets with large density

IF 0.8 3区数学

Bulletin of the London Mathematical Society Pub Date : 2024-11-08 DOI: 10.1112/blms.13180

Ioannis Kousek, Tristán Radić

{"title":"Infinite unrestricted sumsets of the form \u0000 \u0000 \u0000 B\u0000 +\u0000 B\u0000 \u0000 $B+B$\u0000 in sets with large density","authors":"Ioannis Kousek, Tristán Radić","doi":"10.1112/blms.13180","DOIUrl":"https://doi.org/10.1112/blms.13180","url":null,"abstract":"For a set <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>A</mi>\u0000 <mo>⊂</mo>\u0000 <mi>N</mi>\u0000 </mrow>\u0000 <annotation>$A subset {mathbb {N}}$</annotation>\u0000 </semantics></math>, we characterize the existence of an infinite set <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>B</mi>\u0000 <mo>⊂</mo>\u0000 <mi>N</mi>\u0000 </mrow>\u0000 <annotation>$B subset {mathbb {N}}$</annotation>\u0000 </semantics></math> and <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>t</mi>\u0000 <mo>∈</mo>\u0000 <mo>{</mo>\u0000 <mn>0</mn>\u0000 <mo>,</mo>\u0000 <mn>1</mn>\u0000 <mo>}</mo>\u0000 </mrow>\u0000 <annotation>$t in lbrace 0,1rbrace$</annotation>\u0000 </semantics></math> such that <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>B</mi>\u0000 <mo>+</mo>\u0000 <mi>B</mi>\u0000 <mo>⊂</mo>\u0000 <mi>A</mi>\u0000 <mo>−</mo>\u0000 <mi>t</mi>\u0000 </mrow>\u0000 <annotation>$B+B subset A-t$</annotation>\u0000 </semantics></math>, where <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>B</mi>\u0000 <mo>+</mo>\u0000 <mi>B</mi>\u0000 <mo>=</mo>\u0000 <mo>{</mo>\u0000 <msub>\u0000 <mi>b</mi>\u0000 <mn>1</mn>\u0000 </msub>\u0000 <mo>+</mo>\u0000 <msub>\u0000 <mi>b</mi>\u0000 <mn>2</mn>\u0000 </msub>\u0000 <mo>:</mo>\u0000 <msub>\u0000 <mi>b</mi>\u0000 <mn>1</mn>\u0000 </msub>\u0000 <mo>,</mo>\u0000 <msub>\u0000 <mi>b</mi>\u0000 <mn>2</mn>\u0000 </msub>\u0000 <mo>∈</mo>\u0000 <mi>B</mi>\u0000 <mo>}</mo>\u0000 </mrow>\u0000 <annotation>$B+B =lbrace b_1+b_2colon b_1,b_2 in Brbrace$</annotation>\u0000 </semantics></math>, in terms of the density of the set <math>\u0000 <semantics>\u0000 <mi>A</mi>\u0000 <annotation>$A$</annotation>\u0000 </semantics></math>. Specifically, when the lower density <math>\u0000 <semantics>\u0000 <mrow>\u0000 <munder>\u0000 <mrow>\u0000 <mrow></m","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"57 1","pages":"48-68"},"PeriodicalIF":0.8,"publicationDate":"2024-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/blms.13180","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143113569","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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

Non-cyclicity and polynomials in Dirichlet-type spaces of the unit ball 单位球的dirichlet型空间中的非循环性和多项式

IF 0.8 3区数学

Bulletin of the London Mathematical Society Pub Date : 2024-11-06 DOI: 10.1112/blms.13176

Dimitrios Vavitsas, Konstantinos Zarvalis

引用次数: 0

Hermitian metrics with vanishing second Chern Ricci curvature

IF 0.8 3区数学

Bulletin of the London Mathematical Society Pub Date : 2024-11-06 DOI: 10.1112/blms.13179

Kyle Broder, Artem Pulemotov

引用次数: 0

Continuity of the j $j$ -function on the Markov tree 马尔可夫树上j$ j$ -函数的连续性

IF 0.8 3区数学

Bulletin of the London Mathematical Society Pub Date : 2024-11-01 DOI: 10.1112/blms.13173

Paloma Bengoechea

引用次数: 0

There are no extremal eutactic stars other than root systems

IF 0.8 3区数学

Bulletin of the London Mathematical Society Pub Date : 2024-10-31 DOI: 10.1112/blms.13177

Haowu Wang

引用次数: 0

The covariant functoriality of graph algebras 图代数的协变函数性

IF 0.8 3区数学

Bulletin of the London Mathematical Society Pub Date : 2024-10-28 DOI: 10.1112/blms.13125

Piotr M. Hajac, Mariusz Tobolski

{"title":"The covariant functoriality of graph algebras","authors":"Piotr M. Hajac, Mariusz Tobolski","doi":"10.1112/blms.13125","DOIUrl":"https://doi.org/10.1112/blms.13125","url":null,"abstract":"In the standard category of directed graphs, graph morphisms map edges to edges. By allowing graph morphisms to map edges to finite paths (path homomorphisms of graphs), we obtain an ambient category in which we determine subcategories enjoying covariant functors to categories of algebras given by constructions of path algebras, Cohn path algebras, and Leavitt path algebras, respectively. Thus, we obtain new tools to unravel homomorphisms between Leavitt path algebras and between graph C*-algebras. In particular, a graph-algebraic presentation of the inclusion of the C*-algebra of a quantum real projective plane into the Toeplitz algebra allows us to determine a quantum CW-complex structure of the former. It comes as a mixed-pullback theorem where two <math>\u0000 <semantics>\u0000 <mo>∗</mo>\u0000 <annotation>$*$</annotation>\u0000 </semantics></math>-homomorphisms are covariantly induced from path homomorphisms of graphs and the remaining two are contravariantly induced by admissible inclusions of graphs. As a main result and an application of new covariant-induction tools, we prove such a mixed-pullback theorem for arbitrary graphs whose all vertex-simple loops have exits, which substantially enlarges the scope of examples coming from noncommutative topology.","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"56 11","pages":"3269-3288"},"PeriodicalIF":0.8,"publicationDate":"2024-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142574203","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

Singular loci of algebras over ramified discrete valuation rings 分枝离散估值环上代数的奇异轨迹

IF 0.8 3区数学

Bulletin of the London Mathematical Society Pub Date : 2024-10-21 DOI: 10.1112/blms.13174

Nawaj KC

引用次数: 0

Subgroups of bounded rank in hyperbolic 3-manifold groups 双曲3流形群中有界秩的子群

IF 0.8 3区数学

Bulletin of the London Mathematical Society Pub Date : 2024-10-20 DOI: 10.1112/blms.13170

Ian Biringer

引用次数: 0