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A family of holomorphic functions defined by differential inequality 由微分不等式定义的一组全纯函数
IF 1 4区 数学
Mathematical Inequalities & Applications Pub Date : 2022-01-01 DOI: 10.7153/mia-2022-25-03
N. H. Mohammed, E. A. Adegani, T. Bulboacă, N. Cho
{"title":"A family of holomorphic functions defined by differential inequality","authors":"N. H. Mohammed, E. A. Adegani, T. Bulboacă, N. Cho","doi":"10.7153/mia-2022-25-03","DOIUrl":"https://doi.org/10.7153/mia-2022-25-03","url":null,"abstract":"","PeriodicalId":49868,"journal":{"name":"Mathematical Inequalities & Applications","volume":"1 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71205374","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 5
Boundedness of Riemann-Liouville operator from weighted Sobolev space to weighted Lebesgue space for 1 < q < p < ∞ 1 < q < p <∞时Riemann-Liouville算子从加权Sobolev空间到加权Lebesgue空间的有界性
IF 1 4区 数学
Mathematical Inequalities & Applications Pub Date : 2022-01-01 DOI: 10.7153/mia-2022-25-02
A. Kalybay, R. Oinarov
{"title":"Boundedness of Riemann-Liouville operator from weighted Sobolev space to weighted Lebesgue space for 1 < q < p < ∞","authors":"A. Kalybay, R. Oinarov","doi":"10.7153/mia-2022-25-02","DOIUrl":"https://doi.org/10.7153/mia-2022-25-02","url":null,"abstract":"","PeriodicalId":49868,"journal":{"name":"Mathematical Inequalities & Applications","volume":"1 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71205361","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 3
A simple counterexample for the permanent-on-top conjecture 永久顶猜想的一个简单反例
IF 1 4区 数学
Mathematical Inequalities & Applications Pub Date : 2022-01-01 DOI: 10.7153/mia-2022-25-01
Hoang-Anh Tran
{"title":"A simple counterexample for the permanent-on-top conjecture","authors":"Hoang-Anh Tran","doi":"10.7153/mia-2022-25-01","DOIUrl":"https://doi.org/10.7153/mia-2022-25-01","url":null,"abstract":"","PeriodicalId":49868,"journal":{"name":"Mathematical Inequalities & Applications","volume":"1 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71205032","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Regularity of commutators of multilinear maximal operators with Lipschitz symbols 带Lipschitz符号的多线性极大算子的换易子的正则性
IF 1 4区 数学
Mathematical Inequalities & Applications Pub Date : 2022-01-01 DOI: 10.7153/mia-2022-25-08
Ting Chen, Feng Liu
{"title":"Regularity of commutators of multilinear maximal operators with Lipschitz symbols","authors":"Ting Chen, Feng Liu","doi":"10.7153/mia-2022-25-08","DOIUrl":"https://doi.org/10.7153/mia-2022-25-08","url":null,"abstract":". We study the regularity properties for commutators of multilinear fractional maximal operators. More precisely, let m (cid:2) 1, 0 (cid:3) α < mn and (cid:2) b = ( b 1 ,..., b m ) with each b i belonging to the Lipschitz space Lip ( R ) , we denote by [ (cid:2) b , M α ] (resp., M α ,(cid:2) b ) the commutator of the multilinear fractional maximal operator M α with (cid:2) b (resp., the multilinear fractional maximal commutators). When α = 0, we denote [ (cid:2) b , M α ] = [ (cid:2) b , M ] and M α ,(cid:2) b = M (cid:2) b . We show that for 0 < s < 1, 1 < p 1 ,..., p m , p , q < ∞ , 1 / p = 1 / p 1 + ··· + 1 / p m , both [ (cid:2) b , M ] and M (cid:2) b are bounded and continuous from W s , p 1 ( R n ) ×···× W s , p m ( R n ) to W s , p ( R n ) , from F p 1 , q s ( R n ) × ···× F p m , q s ( R n ) to F p , q s ( R n ) and from B p 1 , q s ( R n ) ×···× B p m , q s ( R n ) to B p , q s ( R n ) . It was also shown that for 0 (cid:3) α < mn , 1 < p 1 ,..., p m , q < ∞ and 1 / q = 1 / p 1 + ··· + 1 / p m − α / n , both [ (cid:2) b , M ] and M (cid:2) b are W 1 , p 1 ( R n ) ×···× W 1 , p m ( R n ) to W 1 , q ( R n ) .","PeriodicalId":49868,"journal":{"name":"Mathematical Inequalities & Applications","volume":"1 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71205319","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 boundedness of the Hardy-Littlewood maximal and Calderón-Zygmund operators on Orlicz-Morrey and weak Orlicz-Morrey spaces Orlicz-Morrey空间上Hardy-Littlewood极大算子和Calderón-Zygmund算子的加权有界性
IF 1 4区 数学
Mathematical Inequalities & Applications Pub Date : 2021-08-16 DOI: 10.7153/mia-2021-24-81
Ryota Kawasumi, E. Nakai
{"title":"Weighted boundedness of the Hardy-Littlewood maximal and Calderón-Zygmund operators on Orlicz-Morrey and weak Orlicz-Morrey spaces","authors":"Ryota Kawasumi, E. Nakai","doi":"10.7153/mia-2021-24-81","DOIUrl":"https://doi.org/10.7153/mia-2021-24-81","url":null,"abstract":"For the Hardy-Littlewood maximal and Calder´on-Zygmund operators, the weighted boundedness on the Lebesgue spaces are well known. We extend these to the Orlicz-Morrey spaces. Moreover, we prove the weighted boundedness on the weak Orlicz-Morrey spaces. To do this we show the weak-weak modular inequality. The Orlicz-Morrey space and its weak version contain weighted Orlicz, Morrey and Lebesgue spaces and their weak versions as special cases. Then we also get the boundedness for these function spaces as corollaries.","PeriodicalId":49868,"journal":{"name":"Mathematical Inequalities & Applications","volume":" ","pages":""},"PeriodicalIF":1.0,"publicationDate":"2021-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41808271","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 1
Norm of the discrete Cesàaro operator minus identity 离散Cesàaro算子的范数减去恒等式
IF 1 4区 数学
Mathematical Inequalities & Applications Pub Date : 2021-05-29 DOI: 10.7153/mia-2022-25-04
G. Sinnamon
{"title":"Norm of the discrete Cesàaro operator minus identity","authors":"G. Sinnamon","doi":"10.7153/mia-2022-25-04","DOIUrl":"https://doi.org/10.7153/mia-2022-25-04","url":null,"abstract":"The norm of C−I on l, where C is the Cesàro operator, is shown to be 1/(p − 1) when 1 < p ≤ 2. This verifies a recent conjecture of G. J. O. Jameson. The norm of C − I on l is also determined when 2 < p < ∞. The two parts together answer a question raised by G. Bennett in 1996. Operator norms in the continuous case, Hardy’s averaging operator minus identity, are already known. Norms in the discrete and continuous cases coincide. The Cesàro operator, C, maps a sequence (xn) to (yn), where yn = 1 n n","PeriodicalId":49868,"journal":{"name":"Mathematical Inequalities & Applications","volume":" ","pages":""},"PeriodicalIF":1.0,"publicationDate":"2021-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44549536","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 5
On the Hardy property of mixed means 关于混合均值的Hardy性质
IF 1 4区 数学
Mathematical Inequalities & Applications Pub Date : 2021-04-12 DOI: 10.7153/mia-2021-24-60
P. Pasteczka
{"title":"On the Hardy property of mixed means","authors":"P. Pasteczka","doi":"10.7153/mia-2021-24-60","DOIUrl":"https://doi.org/10.7153/mia-2021-24-60","url":null,"abstract":". Hardy property of means has been extensively studied by Páles and Pasteczka since 2016. The core of this research is based on few of their properties: concavity, symmetry, monotonicity, repetition invariance and homogeneity (last axiom was recently omitted using some homogenizations techniques). In the present paper we deliver a study of possible omitting monotonicity and replacing repetition invariance by a weaker axiom. These results are then used to establish the Hardy constant for certain types of mixed means.","PeriodicalId":49868,"journal":{"name":"Mathematical Inequalities & Applications","volume":" ","pages":""},"PeriodicalIF":1.0,"publicationDate":"2021-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49612642","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 2
Remark on the Chain rule of fractional derivative in the Sobolev framework Sobolev框架下分数阶导数的链式法则
IF 1 4区 数学
Mathematical Inequalities & Applications Pub Date : 2021-04-11 DOI: 10.7153/mia-2021-24-77
K. Fujiwara
{"title":"Remark on the Chain rule of fractional derivative in the Sobolev framework","authors":"K. Fujiwara","doi":"10.7153/mia-2021-24-77","DOIUrl":"https://doi.org/10.7153/mia-2021-24-77","url":null,"abstract":"A chain rule for power product is studied with fractional differential operators in the framework of Sobolev spaces. The fractional differential operators are defined by the Fourier multipliers. The chain rule is considered newly in the case where the order of differential operators is between one and two. The study is based on the analogy of the classical chain rule or Leibniz rule.","PeriodicalId":49868,"journal":{"name":"Mathematical Inequalities & Applications","volume":" ","pages":""},"PeriodicalIF":1.0,"publicationDate":"2021-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42643281","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 2
Exact converses to a reverse AM-GM inequality, with applications to sums of independent random variables and (super)martingales 精确的逆AM-GM不等式，应用于独立随机变量和(超)鞅的和
IF 1 4区 数学
Mathematical Inequalities & Applications Pub Date : 2021-03-29 DOI: 10.7153/MIA-2021-24-40
I. Pinelis
{"title":"Exact converses to a reverse AM-GM inequality, with applications to sums of independent random variables and (super)martingales","authors":"I. Pinelis","doi":"10.7153/MIA-2021-24-40","DOIUrl":"https://doi.org/10.7153/MIA-2021-24-40","url":null,"abstract":"For every given real value of the ratio $mu:=A_X/G_X>1$ of the arithmetic and geometric means of a positive random variable $X$ and every real $v>0$, exact upper bounds on the right- and left-tail probabilities $mathsf{P}(X/G_Xge v)$ and $mathsf{P}(X/G_Xle v)$ are obtained, in terms of $mu$ and $v$. In particular, these bounds imply that $X/G_Xto1$ in probability as $A_X/G_Xdownarrow1$. Such a result may be viewed as a converse to a reverse Jensen inequality for the strictly concave function $f=ln$, whereas the well-known Cantelli and Chebyshev inequalities may be viewed as converses to a reverse Jensen inequality for the strictly concave quadratic function $f(x) equiv -x^2$. As applications of the mentioned new results, improvements of the Markov, Bernstein--Chernoff, sub-Gaussian, and Bennett--Hoeffding probability inequalities are given.","PeriodicalId":49868,"journal":{"name":"Mathematical Inequalities & Applications","volume":" ","pages":""},"PeriodicalIF":1.0,"publicationDate":"2021-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48610376","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
The ℓ_p-norm of C-I, where C is the Cesàro operator C- i的p范数，其中C是Cesàro算子
IF 1 4区 数学
Mathematical Inequalities & Applications Pub Date : 2021-02-19 DOI: 10.7153/MIA-2021-24-38
G. Jameson
{"title":"The ℓ_p-norm of C-I, where C is the Cesàro operator","authors":"G. Jameson","doi":"10.7153/MIA-2021-24-38","DOIUrl":"https://doi.org/10.7153/MIA-2021-24-38","url":null,"abstract":"For the Cesaro operator C, it is known that ||C-I||_2 = 1. Here we prove that ||C-I||_4 < 3^(1/4) and ||C^T-I||_4 = 3. Bounds for intermediate values of p are derived from the Riesz-Thorin interpolation theorem. An estimate for lower bounds is obtained.","PeriodicalId":49868,"journal":{"name":"Mathematical Inequalities & Applications","volume":"1 1","pages":"551-557"},"PeriodicalIF":1.0,"publicationDate":"2021-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42871635","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 4
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