Nikishin’s theorem and factorization through Marcinkiewicz spaces

IF 0.8 3区数学 Q2 MATHEMATICS Proceedings of the American Mathematical Society Pub Date : 2024-04-19 DOI:10.1090/proc/16888

Mieczysław Mastyło, Enrique Sánchez Pérez

{"title":"Nikishin’s theorem and factorization through Marcinkiewicz spaces","authors":"Mieczysław Mastyło, Enrique Sánchez Pérez","doi":"10.1090/proc/16888","DOIUrl":null,"url":null,"abstract":"<p>Consider <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper L Superscript 0\"> <mml:semantics> <mml:msup> <mml:mi>L</mml:mi> <mml:mn>0</mml:mn> </mml:msup> <mml:annotation encoding=\"application/x-tex\">L^0</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, the <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper F\"> <mml:semantics> <mml:mi>F</mml:mi> <mml:annotation encoding=\"application/x-tex\">F</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-space of all equivalence classes of measurable functions on a finite measure space equipped with the topology of convergence in measure. Inspired by Nikishin’s classical result on the factorization of sublinear continuous operators from a Banach space to <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper L Superscript 0\"> <mml:semantics> <mml:msup> <mml:mi>L</mml:mi> <mml:mn>0</mml:mn> </mml:msup> <mml:annotation encoding=\"application/x-tex\">L^0</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, we prove a theorem that characterizes those maps from any quasi-metric space into <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper L Superscript 0\"> <mml:semantics> <mml:msup> <mml:mi>L</mml:mi> <mml:mn>0</mml:mn> </mml:msup> <mml:annotation encoding=\"application/x-tex\">L^0</mml:annotation> </mml:semantics> </mml:math> </inline-formula> that factor strongly through Marcinkiewicz weighted spaces. We show applications to sublinear operators on a certain class of quasi-Banach spaces with generalized Rademacher type generated by Orlicz sequence spaces.</p>","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":"39 1","pages":""},"PeriodicalIF":0.8000,"publicationDate":"2024-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the American Mathematical Society","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1090/proc/16888","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

Consider L 0 L^0 , the F F -space of all equivalence classes of measurable functions on a finite measure space equipped with the topology of convergence in measure. Inspired by Nikishin’s classical result on the factorization of sublinear continuous operators from a Banach space to L 0 L^0 , we prove a theorem that characterizes those maps from any quasi-metric space into L 0 L^0 that factor strongly through Marcinkiewicz weighted spaces. We show applications to sublinear operators on a certain class of quasi-Banach spaces with generalized Rademacher type generated by Orlicz sequence spaces.

查看原文

微信好友朋友圈 QQ好友复制链接

本刊更多论文

尼基申定理和通过马辛凯维奇空间的因式分解

L 0 L^0 是有限度量空间上可测函数的所有等价类的 F F 空间，具有度量收敛拓扑。受尼基申关于从巴纳赫空间到 L 0 L^0 的亚线性连续算子因子化的经典结果的启发，我们证明了一个定理，它描述了从任何准度量空间到 L 0 L^0 的映射的特征，这些映射通过 Marcinkiewicz 加权空间强因子化。我们展示了对某类由奥利奇序列空间生成的广义拉德马赫型准巴纳赫空间上的亚线性算子的应用。

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分钟内获得全文去求助

来源期刊

Proceedings of the American Mathematical Society 数学-数学

CiteScore

1.70

自引率

10.00%

发文量

207

审稿时长

2-4 weeks

期刊介绍： All articles submitted to this journal are peer-reviewed. The AMS has a single blind peer-review process in which the reviewers know who the authors of the manuscript are, but the authors do not have access to the information on who the peer reviewers are. This journal is devoted to shorter research articles (not to exceed 15 printed pages) in all areas of pure and applied mathematics. To be published in the Proceedings, a paper must be correct, new, and significant. Further, it must be well written and of interest to a substantial number of mathematicians. Piecemeal results, such as an inconclusive step toward an unproved major theorem or a minor variation on a known result, are in general not acceptable for publication. Longer papers may be submitted to the Transactions of the American Mathematical Society. Published pages are the same size as those generated in the style files provided for AMS-LaTeX.

期刊最新文献

Almost complex torus manifolds - a problem of Petrie type Elliptic equations with matrix weights and measurable nonlinearities on nonsmooth domains A variance-sensitive Gaussian concentration inequality A short note on 𝜋₁(𝐷𝑖𝑓𝑓_{∂}𝐷^{4𝑘}) for 𝑘≥3 Yosida distance and existence of invariant manifolds in the infinite-dimensional dynamical systems