{"title":"某些分形函数的导数和分形布洛赫型函数的界限","authors":"Bappaditya Bhowmik, Sambhunath Sen","doi":"10.21136/cmj.2024.0332-23","DOIUrl":null,"url":null,"abstract":"<p>It is known that if f is holomorphic in the open unit disc <span>\\(\\mathbb{D}\\)</span> of the complex plane and if, for some <i>c</i> > 0, ∣<i>f</i>(<i>z</i>)∣ ⩽ 1/(1−∣<i>z</i>∣<sup>2</sup>)<sup><i>c</i></sup>, <span>\\(z \\in \\mathbb{D}\\)</span>, then ∣<i>f</i>′(<i>z</i>)∣ ⩽ 2(<i>c</i>+1)/(1−∣<i>z</i>∣<sup>2</sup>)<sup><i>c</i>+1</sup>. We consider a meromorphic analogue of this result. Furthermore, we introduce and study the class of meromorphic Bloch-type functions that possess a nonzero simple pole in D. In particular, we obtain bounds for the modulus of the Taylor coefficients of functions in this class.</p>","PeriodicalId":50596,"journal":{"name":"Czechoslovak Mathematical Journal","volume":"78 1","pages":""},"PeriodicalIF":0.4000,"publicationDate":"2024-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Bounds for the derivative of certain meromorphic functions and on meromorphic Bloch-type functions\",\"authors\":\"Bappaditya Bhowmik, Sambhunath Sen\",\"doi\":\"10.21136/cmj.2024.0332-23\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>It is known that if f is holomorphic in the open unit disc <span>\\\\(\\\\mathbb{D}\\\\)</span> of the complex plane and if, for some <i>c</i> > 0, ∣<i>f</i>(<i>z</i>)∣ ⩽ 1/(1−∣<i>z</i>∣<sup>2</sup>)<sup><i>c</i></sup>, <span>\\\\(z \\\\in \\\\mathbb{D}\\\\)</span>, then ∣<i>f</i>′(<i>z</i>)∣ ⩽ 2(<i>c</i>+1)/(1−∣<i>z</i>∣<sup>2</sup>)<sup><i>c</i>+1</sup>. We consider a meromorphic analogue of this result. Furthermore, we introduce and study the class of meromorphic Bloch-type functions that possess a nonzero simple pole in D. In particular, we obtain bounds for the modulus of the Taylor coefficients of functions in this class.</p>\",\"PeriodicalId\":50596,\"journal\":{\"name\":\"Czechoslovak Mathematical Journal\",\"volume\":\"78 1\",\"pages\":\"\"},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2024-05-31\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Czechoslovak Mathematical Journal\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.21136/cmj.2024.0332-23\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Czechoslovak Mathematical Journal","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.21136/cmj.2024.0332-23","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
摘要
众所周知，如果 f 在复平面的开放单位圆盘 （\mathbb{D}\）中是全态的，并且对于某些 c >；0，∣f(z)∣ ⩽ 1/(1-∣z∣2)c, \(z \in \mathbb{D}\)，那么∣f′(z)∣ ⩽ 2(c+1)/(1-∣z∣2)c+1。我们考虑了这一结果的分形类似物。此外，我们还引入并研究了一类在 D 中具有非零简单极点的布洛赫类函数。
Bounds for the derivative of certain meromorphic functions and on meromorphic Bloch-type functions
It is known that if f is holomorphic in the open unit disc \(\mathbb{D}\) of the complex plane and if, for some c > 0, ∣f(z)∣ ⩽ 1/(1−∣z∣2)c, \(z \in \mathbb{D}\), then ∣f′(z)∣ ⩽ 2(c+1)/(1−∣z∣2)c+1. We consider a meromorphic analogue of this result. Furthermore, we introduce and study the class of meromorphic Bloch-type functions that possess a nonzero simple pole in D. In particular, we obtain bounds for the modulus of the Taylor coefficients of functions in this class.
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