Bloch functions with wild boundary behavior in C N ${\mathbb {C}}^N$

IF 0.9 3区数学 Q2 MATHEMATICS

Bulletin of the London Mathematical Society Pub Date : 2025-04-02 DOI:10.1112/blms.70055

Stéphane Charpentier, Nicolas Espoullier, Rachid Zarouf

{"title":"Bloch functions with wild boundary behavior in \n \n \n C\n N\n \n ${\\mathbb {C}}^N$","authors":"Stéphane Charpentier, Nicolas Espoullier, Rachid Zarouf","doi":"10.1112/blms.70055","DOIUrl":null,"url":null,"abstract":"We prove the existence of functions <math>\n <semantics>\n <mi>f</mi>\n <annotation>$f$</annotation>\n </semantics></math> in the Bloch space of the unit ball <math>\n <semantics>\n <msub>\n <mi>B</mi>\n <mi>N</mi>\n </msub>\n <annotation>${\\mathbb {B}}_N$</annotation>\n </semantics></math> of <math>\n <semantics>\n <msup>\n <mi>C</mi>\n <mi>N</mi>\n </msup>\n <annotation>${\\mathbb {C}}^N$</annotation>\n </semantics></math> with the property that, given any measurable function <math>\n <semantics>\n <mi>φ</mi>\n <annotation>$\\varphi$</annotation>\n </semantics></math> on the unit sphere <math>\n <semantics>\n <msub>\n <mi>S</mi>\n <mi>N</mi>\n </msub>\n <annotation>${\\mathbb {S}}_N$</annotation>\n </semantics></math>, there exists a sequence <math>\n <semantics>\n <msub>\n <mrow>\n <mo>(</mo>\n <msub>\n <mi>r</mi>\n <mi>n</mi>\n </msub>\n <mo>)</mo>\n </mrow>\n <mi>n</mi>\n </msub>\n <annotation>$(r_n)_n$</annotation>\n </semantics></math>, <math>\n <semantics>\n <mrow>\n <msub>\n <mi>r</mi>\n <mi>n</mi>\n </msub>\n <mo>∈</mo>\n <mrow>\n <mo>(</mo>\n <mn>0</mn>\n <mo>,</mo>\n <mn>1</mn>\n <mo>)</mo>\n </mrow>\n </mrow>\n <annotation>$r_n\\in (0,1)$</annotation>\n </semantics></math>, converging to 1, such that for every <math>\n <semantics>\n <mrow>\n <mi>w</mi>\n <mo>∈</mo>\n <msub>\n <mi>B</mi>\n <mi>N</mi>\n </msub>\n </mrow>\n <annotation>$w\\in {\\mathbb {B}}_N$</annotation>\n </semantics></math>,\n\n ","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"57 6","pages":"1691-1707"},"PeriodicalIF":0.9000,"publicationDate":"2025-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Bulletin of the London Mathematical Society","FirstCategoryId":"100","ListUrlMain":"https://londmathsoc.onlinelibrary.wiley.com/doi/10.1112/blms.70055","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

Abstract

We prove the existence of functions $f$ in the Bloch space of the unit ball $B_{N}$ of $C^{N}$ with the property that, given any measurable function $φ$ on the unit sphere $S_{N}$ , there exists a sequence ${(r_{n})}_{n}$ , $r_{n} \in (0, 1)$ , converging to 1, such that for every $w \in B_{N}$ ,

Abstract Image

查看原文本刊更多论文

C ${\mathbb {C}}^N$

证明了C N$ {\mathbb {C}}^N$的单位球B N$ {\mathbb {B}}_N$的Bloch空间中函数f$ f$的存在性，其性质是：给定单位球面上任意可测函数φ $\varphi$ {\mathbb {S}}_N$，存在一个序列（r n） n$ (r_n)_n$，R n∈(0,1)$ r_n\in(0,1)$，收敛于1，使得对于每个w∈B N$ w\in {\mathbb {B}}_N$，

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊