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Mathematical Inequalities & Applications最新文献

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An intertwined Cauchy-Schwarz-type inequality based on a Lagrange-type identity 基于拉格朗日型恒等式的交织柯西-施瓦茨型不等式
Mathematical Inequalities & Applications Pub Date : 2023-03-06 DOI: 10.7153/mia-2023-26-19
I. Pinelis
{"title":"An intertwined Cauchy-Schwarz-type inequality based on a Lagrange-type identity","authors":"I. Pinelis","doi":"10.7153/mia-2023-26-19","DOIUrl":"https://doi.org/10.7153/mia-2023-26-19","url":null,"abstract":"Based on an apparently new Lagrange-type identity, a Cauchy--Schwarz-type inequality is proved. The mentioned identity is obtained by using certain ``macro'' variables; it is hoped that such a method can be used to prove or produce other identities and inequalities.","PeriodicalId":122217,"journal":{"name":"Mathematical Inequalities & Applications","volume":"81 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130939978","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
New orders among Hilbert space operators 希尔伯特空间算子的新秩序
Mathematical Inequalities & Applications Pub Date : 2022-12-13 DOI: 10.7153/mia-2023-26-27
M. Sababheh, H. Moradi
{"title":"New orders among Hilbert space operators","authors":"M. Sababheh, H. Moradi","doi":"10.7153/mia-2023-26-27","DOIUrl":"https://doi.org/10.7153/mia-2023-26-27","url":null,"abstract":"This article introduces several new relations among related Hilbert space operators. In particular, we prove some L\"{o}ewner partial orderings among $T, |T|, mathcal{R}T, mathcal{I}T, |T|+|T^*|$ and many other related forms, as a new discussion in this field; where $mathcal{R}T$ and $mathcal{I}T$ are the real and imaginary parts of the operator $T$. Our approach will be based on proving the positivity of some new matrix operators, where several new forms for positive matrix operators will be presented as a key tool in obtaining the other ordering results. As an application, we present some results treating numerical radius inequalities in a way that extends some known results in this direction, in addition to some results about the singular values.","PeriodicalId":122217,"journal":{"name":"Mathematical Inequalities & Applications","volume":"105 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132147279","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Inequalities for weighted spaces with variable exponents 变指数加权空间的不等式
Mathematical Inequalities & Applications Pub Date : 2022-11-22 DOI: 10.7153/mia-2023-26-33
P. Rocha
{"title":"Inequalities for weighted spaces with variable exponents","authors":"P. Rocha","doi":"10.7153/mia-2023-26-33","DOIUrl":"https://doi.org/10.7153/mia-2023-26-33","url":null,"abstract":"In this article we obtain an\"off-diagonal\"version of the Fefferman-Stein vector-valued maximal inequality on weighted Lebesgue spaces with variable exponents. As an application of this result and the atomic decomposition developed in [12] we prove, for certain exponents $q(cdot)$ in $mathcal{P}^{log}(mathbb{R}^{n})$ and certain weights $omega$, that the Riesz potential $I_{alpha}$, with $0<alpha<n$, can be extended to a bounded operator from $H^{p(cdot)}_{omega}(mathbb{R}^{n})$ into $L^{q(cdot)}_{omega}(mathbb{R}^{n})$, for $frac{1}{p(cdot)} := frac{1}{q(cdot)} + frac{alpha}{n}$.","PeriodicalId":122217,"journal":{"name":"Mathematical Inequalities &amp; Applications","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115627248","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Dirac inequality for highest weight Harish-Chandra modules II 最大权值Harish-Chandra模的Dirac不等式
Mathematical Inequalities &amp; Applications Pub Date : 2022-09-30 DOI: 10.7153/mia-2023-26-44
Pavle Pandvzi'c, Ana Prli'c, Vladim'ir Souvcek, V'it Tuvcek
{"title":"Dirac inequality for highest weight Harish-Chandra modules II","authors":"Pavle Pandvzi'c, Ana Prli'c, Vladim'ir Souvcek, V'it Tuvcek","doi":"10.7153/mia-2023-26-44","DOIUrl":"https://doi.org/10.7153/mia-2023-26-44","url":null,"abstract":"Let $G$ be a connected simply connected noncompact exceptional simple Lie group of Hermitian type. In this paper, we work with the Dirac inequality which is a very useful tool for the classification of unitary highest weight modules.","PeriodicalId":122217,"journal":{"name":"Mathematical Inequalities &amp; Applications","volume":"49 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127118154","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Dirac inequality for highest weight Harish-Chandra modules I 最大权值Harish-Chandra模的Dirac不等式
Mathematical Inequalities &amp; Applications Pub Date : 2022-09-30 DOI: 10.7153/mia-2023-26-17
Pavle Pandvzi'c, Ana Prli'c, Vladim'ir Souvcek, V'it Tuvcek
{"title":"Dirac inequality for highest weight Harish-Chandra modules I","authors":"Pavle Pandvzi'c, Ana Prli'c, Vladim'ir Souvcek, V'it Tuvcek","doi":"10.7153/mia-2023-26-17","DOIUrl":"https://doi.org/10.7153/mia-2023-26-17","url":null,"abstract":"Let $G$ be a connected simply connected noncompact classical simple Lie group of Hermitian type. Then $G$ has unitary highest weight representations. The proof of the classification of unitary highest weight representations of $G$ given by Enright, Howe and Wallach is based on the Dirac inequality of Parthasarathy, Jantzen's formula and Howe's theory of dual pairs where one group in the pair is compact. In this paper we focus on the Dirac inequality which can be used to prove the classification in a more direct way.","PeriodicalId":122217,"journal":{"name":"Mathematical Inequalities &amp; Applications","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129867556","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Characterizations of Lipschitz functions via the commutators of maximal function in Orlicz spaces on stratified Lie groups 层李群上Orlicz空间中极大函数的对易子刻画Lipschitz函数
Mathematical Inequalities &amp; Applications Pub Date : 2022-07-20 DOI: 10.7153/mia-2023-26-29
V. Guliyev
{"title":"Characterizations of Lipschitz functions via the commutators of maximal function in Orlicz spaces on stratified Lie groups","authors":"V. Guliyev","doi":"10.7153/mia-2023-26-29","DOIUrl":"https://doi.org/10.7153/mia-2023-26-29","url":null,"abstract":"We give necessary and sufficient conditions for the boundedness of the maximal commutators $M_{b}$, the commutators of the maximal operator $[b, M]$ and the commutators of the sharp maximal operator $[b, M^{sharp}]$ in Orlicz spaces $L^{Phi}(mathbb{G})$ on any stratified Lie group $mathbb{G}$ when $b$ belongs to Lipschitz spaces $dot{Lambda}_{beta}(mathbb{G})$. We obtain some new characterizations for certain subclasses of Lipschitz spaces $dot{Lambda}_{beta}(mathbb{G})$.","PeriodicalId":122217,"journal":{"name":"Mathematical Inequalities &amp; Applications","volume":"83 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122658413","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
A sufficient condition for a complex polynomial to have only simple zeros and an analog of Hutchinson's theorem for real polynomials 复多项式只有简单零的充分条件及实多项式的哈金森定理的类比
Mathematical Inequalities &amp; Applications Pub Date : 2022-07-17 DOI: 10.7153/mia-2023-26-06
Kateryna Bielenova, Hryhorii Nazarenko, A. Vishnyakova
{"title":"A sufficient condition for a complex polynomial to have only simple zeros and an analog of Hutchinson's theorem for real polynomials","authors":"Kateryna Bielenova, Hryhorii Nazarenko, A. Vishnyakova","doi":"10.7153/mia-2023-26-06","DOIUrl":"https://doi.org/10.7153/mia-2023-26-06","url":null,"abstract":"We find the constant $b_{infty}$ ($b_{infty} approx 4.81058280$) such that if a complex polynomial or entire function $f(z) = sum_{k=0}^ omega a_k z^k, $ $omega in {2, 3, 4, ldots } cup {infty},$ with nonzero coefficients satisfy the conditions $left|frac{a_k^2}{a_{k-1} a_{k+1}}right|>b_{infty} $ for all $k =1, 2, ldots, omega-1,$ then all the zeros of $f$ are simple. We show that the constant $b_{infty}$ in the statement above is the smallest possible. We also obtain an analog of Hutchinson's theorem for polynomials or entire functions with real nonzero coefficients.","PeriodicalId":122217,"journal":{"name":"Mathematical Inequalities &amp; Applications","volume":"410 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134175288","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
On Ramanujan's prime counting inequality 关于拉马努金的素数计数不等式
Mathematical Inequalities &amp; Applications Pub Date : 2022-07-06 DOI: 10.7153/mia-2022-25-71
Christian Axler
{"title":"On Ramanujan's prime counting inequality","authors":"Christian Axler","doi":"10.7153/mia-2022-25-71","DOIUrl":"https://doi.org/10.7153/mia-2022-25-71","url":null,"abstract":". In this paper, we give a new upper bound for the number N R which is defined to be the smallest positive integer such that a certain inequality due to Ramanujan involving the prime counting function π ( x ) holds for every x ≥ N R .","PeriodicalId":122217,"journal":{"name":"Mathematical Inequalities &amp; Applications","volume":"69 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131812322","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Extensions of democracy-like properties for sequences with gaps 带间隙序列的类民主性质的扩展
Mathematical Inequalities &amp; Applications Pub Date : 2022-05-09 DOI: 10.7153/mia-2022-25-72
M. Berasategui, Pablo M. Bern'a
{"title":"Extensions of democracy-like properties for sequences with gaps","authors":"M. Berasategui, Pablo M. Bern'a","doi":"10.7153/mia-2022-25-72","DOIUrl":"https://doi.org/10.7153/mia-2022-25-72","url":null,"abstract":". In [18], T. Oikhberg introduced and studied variants of the greedy and weak greedy algorithms for sequences with gaps. In this paper, we extend some of the notions that appear naturally in connection with these algorithms to the context of sequences with gaps. In particular, we will consider sequences of natural numbers for which the inequality n k + 1 ≤ C n k or n k + 1 ≤ C + n k holds for a positive constant C and all k , and find conditions under which the extended notions are equivalent their regular counterparts.","PeriodicalId":122217,"journal":{"name":"Mathematical Inequalities &amp; Applications","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127036068","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
A note on the multivariate generalization of a basic simple inequality 一个基本的简单不等式的多元推广的注释
Mathematical Inequalities &amp; Applications Pub Date : 2022-03-15 DOI: 10.7153/mia-2022-25-58
Vasiliki Bitsouni, Nikolaos Gialelis
{"title":"A note on the multivariate generalization of a basic simple inequality","authors":"Vasiliki Bitsouni, Nikolaos Gialelis","doi":"10.7153/mia-2022-25-58","DOIUrl":"https://doi.org/10.7153/mia-2022-25-58","url":null,"abstract":"We introduce the multivariate analogue of the well known inequality 1 + x ≤ e x , for an abstract non negative real number x . The result emerges from the study of the blow up time of certain solutions of the Cauchy problem for a particular ODE. It is also closely related to the notion of completely monotone functions and the theory of divided differences.","PeriodicalId":122217,"journal":{"name":"Mathematical Inequalities &amp; Applications","volume":"360 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115292078","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
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