论加权勒贝格空间有界和无界区域中无零角多项式的（m-th\）导数的行为

IF 1.4 3区数学 Q1 MATHEMATICS

Analysis and Mathematical Physics Pub Date : 2025-04-18 DOI:10.1007/s13324-025-01055-9

F. G. Abdullayev, M. Imashkyzy

{"title":"论加权勒贝格空间有界和无界区域中无零角多项式的（m-th\\）导数的行为","authors":"F. G. Abdullayev, M. Imashkyzy","doi":"10.1007/s13324-025-01055-9","DOIUrl":null,"url":null,"abstract":"<div>In this paper, we study the growth of the \\(m-th\\) (\\(m\\ge 1\\)) derivatives of an arbitrary algebraic polynomial in weighted Lebesgue spaces over the whole complex plane. We first study the growth of the \\(m-th\\) derivatives of an arbitrary algebraic polynomial over unbounded regions of the complex plane, and then we obtain estimates for the growth of the \\(m-th\\) derivatives of this polynomial over the closure of the given region. Combining both estimates, we find estimates for the growth of the \\(m-th\\) derivatives of an arbitrary algebraic polynomial over the whole complex plane.</div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"15 3","pages":""},"PeriodicalIF":1.4000,"publicationDate":"2025-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s13324-025-01055-9.pdf","citationCount":"0","resultStr":"{\"title\":\"On the behavior of \\\\(m-th\\\\) derivatives of polynomials in bounded and unbounded regions without zero angles in weighted Lebesgue spaces\",\"authors\":\"F. G. Abdullayev, M. Imashkyzy\",\"doi\":\"10.1007/s13324-025-01055-9\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div>In this paper, we study the growth of the \\\\(m-th\\\\) (\\\\(m\\\\ge 1\\\\)) derivatives of an arbitrary algebraic polynomial in weighted Lebesgue spaces over the whole complex plane. We first study the growth of the \\\\(m-th\\\\) derivatives of an arbitrary algebraic polynomial over unbounded regions of the complex plane, and then we obtain estimates for the growth of the \\\\(m-th\\\\) derivatives of this polynomial over the closure of the given region. Combining both estimates, we find estimates for the growth of the \\\\(m-th\\\\) derivatives of an arbitrary algebraic polynomial over the whole complex plane.</div>\",\"PeriodicalId\":48860,\"journal\":{\"name\":\"Analysis and Mathematical Physics\",\"volume\":\"15 3\",\"pages\":\"\"},\"PeriodicalIF\":1.4000,\"publicationDate\":\"2025-04-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://link.springer.com/content/pdf/10.1007/s13324-025-01055-9.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Analysis and Mathematical Physics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s13324-025-01055-9\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Analysis and Mathematical Physics","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s13324-025-01055-9","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

本文研究了整个复平面上加权Lebesgue空间中任意代数多项式的\(m-th\) （\(m\ge 1\)）导数的增长。我们首先研究了复平面无界区域上任意代数多项式的\(m-th\)导数的增长，然后我们得到了该多项式的\(m-th\)导数在给定区域闭包上的增长估计。结合这两种估计，我们找到了整个复平面上任意代数多项式\(m-th\)导数增长的估计。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

On the behavior of \(m-th\) derivatives of polynomials in bounded and unbounded regions without zero angles in weighted Lebesgue spaces

In this paper, we study the growth of the \(m-th\) (\(m\ge 1\)) derivatives of an arbitrary algebraic polynomial in weighted Lebesgue spaces over the whole complex plane. We first study the growth of the \(m-th\) derivatives of an arbitrary algebraic polynomial over unbounded regions of the complex plane, and then we obtain estimates for the growth of the \(m-th\) derivatives of this polynomial over the closure of the given region. Combining both estimates, we find estimates for the growth of the \(m-th\) derivatives of an arbitrary algebraic polynomial over the whole complex plane.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Analysis and Mathematical Physics MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.70

自引率

0.00%

发文量

122

期刊介绍： Analysis and Mathematical Physics (AMP) publishes current research results as well as selected high-quality survey articles in real, complex, harmonic; and geometric analysis originating and or having applications in mathematical physics. The journal promotes dialog among specialists in these areas.