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Inequalities for polynomials satisfying $$p(z)equiv z^np(1/z)$$ 满足 $$p(z)equiv z^np(1/z)$$ 的多项式不等式
IF 0.9 3区 数学
Acta Mathematica Hungarica Pub Date : 2024-01-31 DOI: 10.1007/s10474-024-01395-1
A. Dalal, N. K. Govil
{"title":"Inequalities for polynomials satisfying $$p(z)equiv z^np(1/z)$$","authors":"A. Dalal, N. K. Govil","doi":"10.1007/s10474-024-01395-1","DOIUrl":"https://doi.org/10.1007/s10474-024-01395-1","url":null,"abstract":"<p>Finding the sharp estimate of <span>(max_{|z|=1} |p'(z)|)</span> in terms of <span>(max_{|z|=1} |p(z)|)</span> for the class of polynomials p(z) satisfying <span>(p(z) equiv z^n p(1/z))</span> has been a well-known open problem for a long time and many papers in this direction have appeared. The earliest result is due to Govil, Jain and Labelle [9] who proved that for polynomials p(z) satisfying <span>(p(z) equiv z^n p(1/z))</span> and having all the zeros either in left half or right half-plane, the inequality <span>(max_{|z|=1} |p'(z)| le frac{n}{sqrt{2}} max_{|z|=1} |p(z)|)</span> holds. A question was posed whether this inequality is sharp. In this paper, we answer this question in the negative by obtaining a bound sharper than <span>(frac{n}{sqrt{2}})</span>. We also conjecture that for such polynomials </p><span>$$max_{|z|=1} |p'(z)| le Big(frac{n}{sqrt{2}} - frac{sqrt{2}-1}{4}(n-2)Big) max_{|z|=1} |p(z)|$$</span><p> and provide evidence in support of this conjecture.</p>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139646978","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
Some New weak-( $$H_{p}-L_p$$ ) Type Inequalities For Weighted Maximal Operators Of Fejér Means Of Walsh–Fourier Series 沃尔什-傅里叶级数的 Fejér 均值的一些新的弱-( $$H_{p}-L_p$$ ) 型不等式
IF 0.9 3区 数学
Acta Mathematica Hungarica Pub Date : 2023-12-13 DOI: 10.1007/s10474-023-01384-w
D. Baramidze, G. Tephnadze
{"title":"Some New weak-( $$H_{p}-L_p$$ ) Type Inequalities For Weighted Maximal Operators Of Fejér Means Of Walsh–Fourier Series","authors":"D. Baramidze, G. Tephnadze","doi":"10.1007/s10474-023-01384-w","DOIUrl":"https://doi.org/10.1007/s10474-023-01384-w","url":null,"abstract":"<p>We introduce some new weighted maximal operators of the Fejér means of the Walsh–Fourier series. We prove that for some \"optimal\" weights these new operators are bounded from the martingale Hardy space <span>(H_{p}(G))</span> to the space <span>(text{weak-}L_{p}(G))</span> , for <span>(0&lt;p&lt;1/2)</span>. Moreover, we also prove sharpness of this result. As a consequence we obtain some new and well-known results.\u0000</p>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138628503","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
Hardy–Sobolev Inequalities For Riesz Potentials Of Functions In Orlicz Spaces Orlicz 空间中函数的 Riesz 势的 Hardy-Sobolev 不等式
IF 0.9 3区 数学
Acta Mathematica Hungarica Pub Date : 2023-12-13 DOI: 10.1007/s10474-023-01389-5
Y. Mizuta, T. Shimomura
{"title":"Hardy–Sobolev Inequalities For Riesz Potentials Of Functions In Orlicz Spaces","authors":"Y. Mizuta, T. Shimomura","doi":"10.1007/s10474-023-01389-5","DOIUrl":"https://doi.org/10.1007/s10474-023-01389-5","url":null,"abstract":"<p>\u0000We establish a Hardy–Sobolev inequality for Riesz potentials of functions in Orlicz spaces.\u0000</p>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138628778","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
On pseudo-real finite subgroups of $$mathrm{PGL}_3(mathbb{C})$$ 论 $$mathrm{PGL}_3(mathbb{C})$$的伪真实有限子群
IF 0.9 3区 数学
Acta Mathematica Hungarica Pub Date : 2023-12-13 DOI: 10.1007/s10474-023-01383-x
E. Badr, A. El-Guindy
{"title":"On pseudo-real finite subgroups of $$mathrm{PGL}_3(mathbb{C})$$","authors":"E. Badr, A. El-Guindy","doi":"10.1007/s10474-023-01383-x","DOIUrl":"https://doi.org/10.1007/s10474-023-01383-x","url":null,"abstract":"<p>Let <span>(G)</span> be a finite subgroup of <span>( rm PGL_3(mathbb C))</span>, and let <span>(sigma)</span> be the generator\u0000of Gal<span>((mathbb C/ mathbb R))</span>. We say that <span>(G)</span> has a <i>real field of moduli</i> if <span>(sigma G)</span> and <span>(G)</span> are\u0000<span>( rm PGL_3(mathbb C))</span>-conjugates. Furthermore, we say that <span>(mathbb R)</span> is <i>a field of definition for</i> <span>(G)</span> or\u0000that <span>(G)</span> <i>is definable over</i> <span>(mathbb R)</span> if <span>(G)</span> is <span>(textrm{PGL}_3(mathbb C))</span>-conjugate to some <span>(acute{G} ,subset , PGL_3(mathbb R))</span>. In\u0000this situation, we call <span>(acute {G})</span> <i>a model for</i> <span>(G)</span> <i>over</i> <span>(mathbb R)</span>. On the other hand, if <span>(G)</span> has a\u0000real field of moduli but is not definable over <span>(mathbb R)</span>, then we call <span>(G)</span> <i>pseudo-real</i>.</p><p>In this paper, we first show that any finite cyclic subgroup <span>(G = mathbb Z / n mathbb Z)</span> in\u0000<span>( rm PGL_3(mathbb C))</span> has a real field of moduli and we provide a necessary and sufficient condition\u0000for <span>(G = mathbb Z / n mathbb Z)</span> to be definable over <span>(mathbb R)</span>; see Theorems 2.1, 2.2, and 2.3. We\u0000also prove that any dihedral group <span>(D_2n)</span> with <span>(n geq 3)</span> in <span>( rm PGL_3(mathbb C))</span> is definable over <span>(mathbb R)</span>;\u0000see Theorem 2.4. Furthermore, we study all other classes of finite subgroups of\u0000<span>( rm PGL_3(mathbb C))</span>, and show that all of them except <span>(A_4n)</span>, <span>(A_5n)</span> and <span>(S_4n)</span> are pseudo-real; see\u0000Theorems 2.5 and 2.6. Finally, we explore the connection of these notions in group\u0000theory with their analogues in arithmetic geometry; see Theorem 2.7 and Example\u00002.8. As a result, we can say that if <span>(G)</span> is definable over <span>(mathbb R)</span>, then its Jordan\u0000constant <span>(J(G))</span> = 1, 2, 3, 6 or 60.</p>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138628308","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
On p-Groups With Restricted Centralizers 关于具有受限中心点的 p 群
IF 0.9 3区 数学
Acta Mathematica Hungarica Pub Date : 2023-12-13 DOI: 10.1007/s10474-023-01388-6
E. Jabara
{"title":"On p-Groups With Restricted Centralizers","authors":"E. Jabara","doi":"10.1007/s10474-023-01388-6","DOIUrl":"https://doi.org/10.1007/s10474-023-01388-6","url":null,"abstract":"<p>\u0000Let <span>(G)</span> be a <span>(p)</span> -group in which every centralizer is either finite or of finite index. It is shown that if the size of the <span>(FC)</span> -center of <span>(G)</span> is infinite and <span>(G)</span> is not an <span>(FC)</span> -group, then <span>(G)</span> is abelian-by-finite.\u0000</p>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138628509","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
Entropy on quasi-uniform spaces 准均匀空间的熵
IF 0.9 3区 数学
Acta Mathematica Hungarica Pub Date : 2023-12-13 DOI: 10.1007/s10474-023-01387-7
P. Haihambo, O. Olela Otafudu
{"title":"Entropy on quasi-uniform spaces","authors":"P. Haihambo, O. Olela Otafudu","doi":"10.1007/s10474-023-01387-7","DOIUrl":"https://doi.org/10.1007/s10474-023-01387-7","url":null,"abstract":"<p>Quasi-uniform entropy <span>(h_{QU}(psi))</span> is defined for a uniformly\u0000continuous self-map <span>(psi)</span> on a <span>(T_0)</span> quasi-uniform space\u0000<span>((X,mathcal{U}))</span>. Basic properties are proved about this entropy,\u0000and it is shown that the quasi-uniform entropy <span>(h_{QU}(psi ,mathcal{U}))</span> is less than or equal to the uniform entropy <span>(h_U(psi, mathcal{U}^s))</span> of <span>(psi)</span> considered as a uniformly continuous\u0000self-map of the uniform space <span>((X,mathcal{U}^s))</span>, where\u0000<span>(mathcal{U}^s)</span> is the uniformity associated with the\u0000quasi-uniformity <span>(mathcal{U})</span>. Finally, we prove that the\u0000completion theorem for quasi-uniform entropy holds in the class of\u0000all join-compact <span>(T_0)</span> quasi-uniform spaces, that is for\u0000join-compact <span>(T_0)</span> quasi-uniform spaces the entropy of a uniformly\u0000continuous self-map coincides with the entropy of its extension to\u0000the bicompletion.</p>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138628321","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
Weighted inequalities for Fourier multiplier operators of Bochner–Riesz type on $$ mathbb{R} ^2$$ $$ mathbb{R} ^2$$ 上 Bochner-Riesz 型傅立叶乘法算子的加权不等式
IF 0.9 3区 数学
Acta Mathematica Hungarica Pub Date : 2023-12-11 DOI: 10.1007/s10474-023-01390-y
S. Sato
{"title":"Weighted inequalities for Fourier multiplier operators of Bochner–Riesz type on $$ mathbb{R} ^2$$","authors":"S. Sato","doi":"10.1007/s10474-023-01390-y","DOIUrl":"https://doi.org/10.1007/s10474-023-01390-y","url":null,"abstract":"<p>We consider Fourier multipliers in <span>( mathbb{R} ^2)</span> with singularities on certain\u0000curves, which are closely related to the Bochner–Riesz Fourier multipliers.\u0000We prove weighted inequalities and vector valued inequalities for the Fourier multiplier\u0000operators which generalize some known results.</p>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138566349","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
On Polynomial Entropy Of Induced Maps On Symmetric Products 论对称积上诱导映射的多项式熵
IF 0.9 3区 数学
Acta Mathematica Hungarica Pub Date : 2023-12-11 DOI: 10.1007/s10474-023-01386-8
M. Ðorić, J. Katić, B. Lasković
{"title":"On Polynomial Entropy Of Induced Maps On Symmetric Products","authors":"M. Ðorić, J. Katić, B. Lasković","doi":"10.1007/s10474-023-01386-8","DOIUrl":"https://doi.org/10.1007/s10474-023-01386-8","url":null,"abstract":"","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138981515","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
On reciprocal sums of infinitely many arithmetic progressions with increasing prime power moduli 论素数幂模递增的无穷多个算术级数的倒数和
IF 0.9 3区 数学
Acta Mathematica Hungarica Pub Date : 2023-12-11 DOI: 10.1007/s10474-023-01385-9
B. Borsos, A. Kovács, N. Tihanyi
{"title":"On reciprocal sums of infinitely many arithmetic progressions with increasing prime power moduli","authors":"B. Borsos, A. Kovács, N. Tihanyi","doi":"10.1007/s10474-023-01385-9","DOIUrl":"https://doi.org/10.1007/s10474-023-01385-9","url":null,"abstract":"<p>Numbers of the form <span>(kcdot p^n+1)</span> with the restriction <span>(k &lt; p^n)</span> are called generalized Proth numbers. For a fixed prime <i>p</i> we denote them by <span>(mathcal{T}_p)</span>. The underlying structure of <span>(mathcal{T}_2)</span> (Proth numbers) was investigated in [2]. In this paper the authors extend their results to all primes. An efficiently computable upper bound for the reciprocal sum of primes in <span>(mathcal{T}_p)</span> is presented.\u0000All formulae were implemented and verified by the PARI/GP computer algebra system. We show that the asymptotic density of <span>( bigcup_{pin mathcal{P}} mathcal{T}_p)</span> is <span>(log 2)</span>.\u0000</p>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138566467","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
Upper bounds for the size of set systems with a symmetric set of Hamming distances 具有汉明距离对称集的集系统大小的上界
IF 0.9 3区 数学
Acta Mathematica Hungarica Pub Date : 2023-11-03 DOI: 10.1007/s10474-023-01374-y
G. Hegedüs
{"title":"Upper bounds for the size of set systems with a symmetric set of Hamming distances","authors":"G. Hegedüs","doi":"10.1007/s10474-023-01374-y","DOIUrl":"10.1007/s10474-023-01374-y","url":null,"abstract":"<div><p>Let <span>( mathcal{F} subseteq 2^{[n]})</span> be a fixed family of subsets. Let <span>(D( mathcal{F} ))</span> stand for the following set of Hamming distances: \u0000</p><div><div><span>$$D( mathcal{F} ):={d_H(F,G) : F, Gin mathcal{F} , Fneq G}$$</span></div></div><p> .\u0000 \u0000<span>( mathcal{F} )</span> is said to be a Hamming symmetric family, if <span>( mathcal{F} )</span>X implies <span>(n-din D( mathcal{F} ))</span> for each <span>(din D( mathcal{F} ))</span>.\u0000</p><p>We give sharp upper bounds for the size of Hamming symmetric families. Our proof is based on the linear algebra bound method. </p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134878238","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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