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Annals of Functional Analysis最新文献

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Characterizations of (B^u_omega ) type Morrey–Triebel–Lizorkin spaces with variable smoothness and integrability 具有可变平稳性和可整性的 $$B^u_omega $$ 型 Morrey-Triebel-Lizorkin 空间的特征
IF 1.2 3区 数学
Annals of Functional Analysis Pub Date : 2024-08-14 DOI: 10.1007/s43034-024-00384-3
Shengrong Wang, Pengfei Guo, Jingshi Xu
{"title":"Characterizations of (B^u_omega ) type Morrey–Triebel–Lizorkin spaces with variable smoothness and integrability","authors":"Shengrong Wang,&nbsp;Pengfei Guo,&nbsp;Jingshi Xu","doi":"10.1007/s43034-024-00384-3","DOIUrl":"10.1007/s43034-024-00384-3","url":null,"abstract":"<div><p>In this paper, we first obtain Fourier multiplier theorem, the approximation characterization and embedding for <span>(B^u_omega )</span> type Morrey–Triebel–Lizorkin spaces with variable smoothness and integrability. Then, we characterize these spaces via Peetre’s maximal functions, the Lusin area function, and the Littlewood–Paley <span>(g^*_lambda )</span>-function. Finally, we obtain the boundedness of the pseudo-differential operators on these spaces.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142210781","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 higher fixed point theorem for foliations: applications to rigidity and integrality 曲面的高阶定点定理：刚性和积分的应用
IF 1.2 3区 数学
Annals of Functional Analysis Pub Date : 2024-08-09 DOI: 10.1007/s43034-024-00383-4
Moulay Tahar Benameur, James L. Heitsch
{"title":"The higher fixed point theorem for foliations: applications to rigidity and integrality","authors":"Moulay Tahar Benameur,&nbsp;James L. Heitsch","doi":"10.1007/s43034-024-00383-4","DOIUrl":"10.1007/s43034-024-00383-4","url":null,"abstract":"<div><p>We give applications of the higher Lefschetz theorems for foliations of Benameur and Heitsch (J. Funct. Anal. 259:131–173, 2010), primarily involving Haefliger cohomology. These results show that the transverse structures of foliations carry important topological and geometric information. This is in the spirit of the passage from the Atiyah–Singer index theorem for a single compact manifold to their families index theorem, involving a compact fiber bundle over a compact base. For foliations, Haefliger cohomology plays the role that the cohomology of the base space plays in the families index theorem. We obtain highly useful numerical invariants by paring with closed holonomy invariant currents. In particular, we prove that the non-triviality of the higher <span>(widehat{A})</span> class of the foliation in Haefliger cohomology can be an obstruction to the existence of non-trivial leaf-preserving compact connected group actions. We then construct a large collection of examples for which no such actions exist. Finally, we relate our results to Connes’ spectral triples, and prove useful integrality results.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141948437","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
Friedrichs and Kreĭn type extensions in terms of representing maps 从表示映射的角度看弗里德里希和克雷恩型扩展
IF 1.2 3区 数学
Annals of Functional Analysis Pub Date : 2024-08-09 DOI: 10.1007/s43034-024-00380-7
S. Hassi, H. S. V. de Snoo
{"title":"Friedrichs and Kreĭn type extensions in terms of representing maps","authors":"S. Hassi,&nbsp;H. S. V. de Snoo","doi":"10.1007/s43034-024-00380-7","DOIUrl":"10.1007/s43034-024-00380-7","url":null,"abstract":"<div><p>A semibounded operator or relation <i>S</i> in a Hilbert space with lower bound <span>(gamma in {{mathbb {R}}})</span> has a symmetric extension <span>(S_textrm{f}=S , widehat{+} ,({0} times mathrm{mul,}S^*))</span>, the weak Friedrichs extension of <i>S</i>, and a selfadjoint extension <span>(S_{textrm{F}})</span>, the Friedrichs extension of <i>S</i>, that satisfy <span>(S subset S_{textrm{f}} subset S_textrm{F})</span>. The Friedrichs extension <span>(S_{textrm{F}})</span> has lower bound <span>(gamma )</span> and it is the largest semibounded selfadjoint extension of <i>S</i>. Likewise, for each <span>(c le gamma )</span>, the relation <i>S</i> has a weak Kreĭn type extension <span>(S_{textrm{k},c}=S , widehat{+} ,(mathrm{ker,}(S^*-c) times {0}))</span> and Kreĭn type extension <span>(S_{textrm{K},c})</span> of <i>S</i>, that satisfy <span>(S subset S_{textrm{k},c} subset S_{textrm{K},c})</span>. The Kreĭn type extension <span>(S_{textrm{K},c})</span> has lower bound <i>c</i> and it is the smallest semibounded selfadjoint extension of <i>S</i> which is bounded below by <i>c</i>. In this paper these special extensions and, more generally, all extremal extensions of <i>S</i> are constructed via the semibounded sesquilinear form <span>({{mathfrak {t}}}(S))</span> that is associated with <i>S</i>; the representing map for the form <span>({{mathfrak {t}}}(S)-c)</span> plays an essential role here.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s43034-024-00380-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141948438","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
Phase-isometries between the positive cones of the Banach space of continuous real-valued functions 连续实值函数巴拿赫空间正锥之间的相位等分线
IF 1.2 3区 数学
Annals of Functional Analysis Pub Date : 2024-08-08 DOI: 10.1007/s43034-024-00378-1
Daisuke Hirota, Izuho Matsuzaki, Takeshi Miura
{"title":"Phase-isometries between the positive cones of the Banach space of continuous real-valued functions","authors":"Daisuke Hirota,&nbsp;Izuho Matsuzaki,&nbsp;Takeshi Miura","doi":"10.1007/s43034-024-00378-1","DOIUrl":"10.1007/s43034-024-00378-1","url":null,"abstract":"<div><p>For a locally compact Hausdorff space <i>L</i>, we denote by <span>(C_0(L,{mathbb {R}}))</span> the Banach space of all continuous real-valued functions on <i>L</i> vanishing at infinity equipped with the supremum norm. We prove that every surjective phase-isometry <span>(T:C_0^+(X,{mathbb {R}})rightarrow C_0^+(Y,{mathbb {R}}))</span> between the positive cones of <span>(C_0(X,{mathbb {R}}))</span> and <span>(C_0(Y,{mathbb {R}}))</span> is a composition operator induced by a homeomorphism between <i>X</i> and <i>Y</i>. Furthermore, we show that any surjective phase-isometry <span>(T:C_0^+(X,{mathbb {R}})rightarrow C_0^+(Y,{mathbb {R}}))</span> extends to a surjective linear isometry from <span>(C_0(X,{mathbb {R}}))</span> onto <span>(C_0(Y,{mathbb {R}}))</span>.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141948441","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
Logarithmic refinements of a power weighted Hardy–Rellich-type inequality 幂加权哈代-雷利克式不等式的对数改进
IF 1.2 3区 数学
Annals of Functional Analysis Pub Date : 2024-08-08 DOI: 10.1007/s43034-024-00381-6
Fritz Gesztesy, Michael M. H. Pang, Jonathan Stanfill
{"title":"Logarithmic refinements of a power weighted Hardy–Rellich-type inequality","authors":"Fritz Gesztesy,&nbsp;Michael M. H. Pang,&nbsp;Jonathan Stanfill","doi":"10.1007/s43034-024-00381-6","DOIUrl":"10.1007/s43034-024-00381-6","url":null,"abstract":"<div><p>The principal purpose of this note is to prove a logarithmic refinement of the power weighted Hardy–Rellich inequality on <i>n</i>-dimensional balls, valid for the largest variety of underlying parameters and for all dimensions <span>(n in {mathbb {N}})</span>, <span>(nge 2)</span>.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s43034-024-00381-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141948439","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
Triangular-(theta ) summability of double Fourier series on quantum tori 量子环上双傅里叶级数的三角- $$theta $$ 可求和性
IF 1.2 3区 数学
Annals of Functional Analysis Pub Date : 2024-07-26 DOI: 10.1007/s43034-024-00376-3
Yong Jiao, Tiantian Zhao, Dejian Zhou
{"title":"Triangular-(theta ) summability of double Fourier series on quantum tori","authors":"Yong Jiao,&nbsp;Tiantian Zhao,&nbsp;Dejian Zhou","doi":"10.1007/s43034-024-00376-3","DOIUrl":"10.1007/s43034-024-00376-3","url":null,"abstract":"<div><p>We study the triangular <span>(theta )</span>-mean of the partial sums of <span>(f in L_{p}({mathbb {T}}_{q}^{2}))</span> and prove the following noncommutative weak and strong type maximal inequalities: </p><div><div><span>$$begin{aligned} Vert (sigma _n^{Delta ,theta }(f))_{nge 1}Vert _{Lambda _{1,infty }({mathbb {T}}_q^2,ell _{infty })}le c_theta Vert fVert _{L_1({mathbb {T}}_{q}^2)},quad p=1 end{aligned}$$</span></div></div><p>and </p><div><div><span>$$begin{aligned} left| left( sigma _{n}^{Delta ,theta }(f)right) _{n ge 1}right| _{L_p({mathbb {T}}_q^2, ell _{infty })} le c_{p, theta }Vert fVert _{L_p({mathbb {T}}_q^2)},quad 1&lt;p&lt;infty , end{aligned}$$</span></div></div><p>where <span>({mathbb {T}}_{q}^{2})</span> is a 2-dimensional quantum torus. As a consequence, we obtain the bilateral almost uniform convergence of <span>(sigma _n^{Delta ,theta }(f))</span> provided <span>(f in L_{p}({mathbb {T}}_{q}^{2}).)</span></p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141775687","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
Extremals of singular Hardy–Trudinger–Moser inequality with remainder terms on unit disc 单位圆盘上带余项的奇异哈代-特鲁丁格-莫泽不等式的极值
IF 1.2 3区 数学
Annals of Functional Analysis Pub Date : 2024-07-16 DOI: 10.1007/s43034-024-00377-2
Weiwei Wang
{"title":"Extremals of singular Hardy–Trudinger–Moser inequality with remainder terms on unit disc","authors":"Weiwei Wang","doi":"10.1007/s43034-024-00377-2","DOIUrl":"10.1007/s43034-024-00377-2","url":null,"abstract":"<div><p>Let <span>(Bsubset {mathbb {R}}^2)</span> be the unit disc, and <span>({mathcal {H}})</span> be the completion of <span>(C_0^infty ({B}))</span> under the norm </p><div><div><span>$$begin{aligned} Vert uVert _{{mathcal {H}}}=Bigg (int _{{B}}|nabla u|^2 {textrm{d}}x- int _{{B}}frac{u^2}{(1-|x|^2)^2}{textrm{d}}xBigg )^{frac{1}{2}}. end{aligned}$$</span></div></div><p>We derive in this paper extremals of singular Hardy–Trudinger–Moser inequality with remainder terms on <i>B</i> using the method of blow-up analysis and rearrangement argument: suppose <span>(0&lt;t&lt;2,)</span> there exists a constant <span>(delta _0&gt;0)</span> such that for <span>(gamma le 4pi (1-t/2)+delta _0)</span> the supremum </p><div><div><span>$$begin{aligned} sup _{uin {mathcal {H}},Vert uVert _{{mathcal {H}}}le 1}int _{{B}}frac{{textrm{e}}^{4pi (1-t/2)u^2}-gamma u^2}{|x|^t} {textrm{d}}x end{aligned}$$</span></div></div><p>can be attained. This extends results of Wang and Ye (Adv Math 230:294–320, 2012) and Yin (Bull Iran Math Soc 49, 2023).</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141715896","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
Criterion for ellipticity on Heisenberg group 海森堡群的椭圆性标准
IF 1.2 3区 数学
Annals of Functional Analysis Pub Date : 2024-07-14 DOI: 10.1007/s43034-024-00375-4
Dmitriy Zanin
{"title":"Criterion for ellipticity on Heisenberg group","authors":"Dmitriy Zanin","doi":"10.1007/s43034-024-00375-4","DOIUrl":"10.1007/s43034-024-00375-4","url":null,"abstract":"<div><p>We provide a semi-constructive criterion for ellipticity of the differential operator on the Heisenberg group <span>(mathbb {H}^1.)</span></p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s43034-024-00375-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141614069","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
A universal property of semigroup (C^*)-algebras generated by cones in groups of rationals 有理群中由锥形生成的半群 $$C^*$$ 算法的一个普遍属性
IF 1.2 3区 数学
Annals of Functional Analysis Pub Date : 2024-07-08 DOI: 10.1007/s43034-024-00374-5
Renat Gumerov, Anatoliy Kuklin, Ekaterina Lipacheva
{"title":"A universal property of semigroup (C^*)-algebras generated by cones in groups of rationals","authors":"Renat Gumerov,&nbsp;Anatoliy Kuklin,&nbsp;Ekaterina Lipacheva","doi":"10.1007/s43034-024-00374-5","DOIUrl":"10.1007/s43034-024-00374-5","url":null,"abstract":"<div><p>The article deals with the reduced semigroup <span>(C^*)</span>-algebras for the positive cones in ordered abelian groups. These <span>(C^*)</span>-algebras are generated by the regular isometric representations of the cones. Using the universal property of the isometric representations for the positive cones, we treat the reduced semigroup <span>(C^*)</span>-algebras as the universal <span>(C^*)</span>-algebras which are defined by sets of generators subject to relations. For arbitrary sequences of prime numbers, we consider the ordered groups of rational numbers determined by these sequences and the reduced semigroup <span>(C^*)</span>-algebras of the positive cones in these groups. It is shown that such an algebra can be characterized as a universal <span>(C^*)</span>-algebra generated by a countable set of isometries subject to polynomial relations associated with a sequence of prime numbers.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141571684","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
Complex interpolation between noncommutative martingale BMO spaces and Hardy–Orlicz spaces 非交换鞅 BMO 空间与 Hardy-Orlicz 空间之间的复插值法
IF 1.2 3区 数学
Annals of Functional Analysis Pub Date : 2024-06-22 DOI: 10.1007/s43034-024-00373-6
Mixuan Hou, Cuiting Li, Guangheng Xie, Yahui Zuo
{"title":"Complex interpolation between noncommutative martingale BMO spaces and Hardy–Orlicz spaces","authors":"Mixuan Hou,&nbsp;Cuiting Li,&nbsp;Guangheng Xie,&nbsp;Yahui Zuo","doi":"10.1007/s43034-024-00373-6","DOIUrl":"10.1007/s43034-024-00373-6","url":null,"abstract":"<div><p>Let <span>(mathcal {M})</span> be a semifinite von Neumann algebra and <span>((mathcal {M}_n)_{nge 0})</span> a nondecreasing filtration of von Neumann subalgebras of <span>(mathcal {M})</span>. Suppose that <span>(Phi )</span> is a <i>p</i>-convex and <i>q</i>-concave Orlicz function with <span>(1&lt; ple q &lt;infty )</span>. In this paper, we establish the complex interpolation between the column martingale little BMO space <span>(textrm{bmo}^c(mathcal {M}))</span> and the noncommutative column conditioned martingale Hardy–Orlicz space <span>(h_{Phi }^c(mathcal {M}))</span> associated with the filtration <span>((mathcal {M}_n)_{nge 0})</span>.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141551645","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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