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Some Hardy-type inequalities in Banach function spaces Banach函数空间中的hardy型不等式
IF 1 4区 数学
Mathematical Inequalities & Applications Pub Date : 2021-01-01 DOI: 10.7153/mia-2021-24-70
Sorina Barza, L. Nikolova, L. Persson, M. Yimer
{"title":"Some Hardy-type inequalities in Banach function spaces","authors":"Sorina Barza, L. Nikolova, L. Persson, M. Yimer","doi":"10.7153/mia-2021-24-70","DOIUrl":"https://doi.org/10.7153/mia-2021-24-70","url":null,"abstract":"","PeriodicalId":49868,"journal":{"name":"Mathematical Inequalities & Applications","volume":"1 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71204704","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
Splitting of operators for frame inequalities 坐标系不等式算子的分裂
IF 1 4区 数学
Mathematical Inequalities & Applications Pub Date : 2021-01-01 DOI: 10.7153/MIA-2021-24-29
Dongwei Li
{"title":"Splitting of operators for frame inequalities","authors":"Dongwei Li","doi":"10.7153/MIA-2021-24-29","DOIUrl":"https://doi.org/10.7153/MIA-2021-24-29","url":null,"abstract":"","PeriodicalId":49868,"journal":{"name":"Mathematical Inequalities & Applications","volume":"1 1","pages":"421-430"},"PeriodicalIF":1.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71204132","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
A note on weighted estimates for bilinear fractional integral operators 双线性分数阶积分算子的加权估计
IF 1 4区 数学
Mathematical Inequalities & Applications Pub Date : 2021-01-01 DOI: 10.7153/MIA-2021-24-35
Y. Komori‐Furuya
{"title":"A note on weighted estimates for bilinear fractional integral operators","authors":"Y. Komori‐Furuya","doi":"10.7153/MIA-2021-24-35","DOIUrl":"https://doi.org/10.7153/MIA-2021-24-35","url":null,"abstract":". De Napoli, Drelichman and Dur´an (2011) proved weighted estimates for the fractional integral operators. Komori-Furuya and Sato (2020) proved weighted estimates for bilinear fractional integral operators. We show that their results are optimal by giving counterexamples. Mathematics subject classi fi cation (2010): 42B20, 42B25.","PeriodicalId":49868,"journal":{"name":"Mathematical Inequalities & Applications","volume":"30 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71204373","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
A Trudinger-Moser inequality with mean value zero on a compact Riemann surface with boundary 具有边界的紧黎曼曲面上均值为零的Trudinger-Moser不等式
IF 1 4区 数学
Mathematical Inequalities & Applications Pub Date : 2020-12-02 DOI: 10.7153/mia-2021-24-54
Mengjie Zhang
{"title":"A Trudinger-Moser inequality with mean value zero on a compact Riemann surface with boundary","authors":"Mengjie Zhang","doi":"10.7153/mia-2021-24-54","DOIUrl":"https://doi.org/10.7153/mia-2021-24-54","url":null,"abstract":"In this paper, on a compact Riemann surface $(Sigma, g)$ with smooth boundary $partialSigma$, we concern a Trudinger-Moser inequality with mean value zero. To be exact, let $lambda_1(Sigma)$ denotes the first eigenvalue of the Laplace-Beltrami operator with respect to the zero mean value condition and $mathcal{ S }= left{ u in W^{1,2} (Sigma, g) : |nabla_g u|_2^2 leq 1right.$ and $left.int_Sigma u ,dv_g = 0 right },$ where $W^{1,2}(Sigma, g)$ is the usual Sobolev space, $|cdot|_2$ denotes the standard $L^2$-norm and $nabla_{g}$ represent the gradient. By the method of blow-up analysis, we obtain begin{eqnarray*} sup_{u in mathcal{S}} int_{Sigma} e^{ 2pi u^{2} left(1+alpha|u|_2^{2}right) }d v_{g} 0$. Based on the similar work in the Euclidean space, which was accomplished by Lu-Yang cite{Lu-Yang}, we strengthen the result of Yang cite{Yang2006IJM}.","PeriodicalId":49868,"journal":{"name":"Mathematical Inequalities & Applications","volume":" ","pages":""},"PeriodicalIF":1.0,"publicationDate":"2020-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49136773","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
Local sharp maximal functions, geometrical maximal functions and rough maximal functions on local Morrey spaces with variable exponents 变指数局部Morrey空间上的局部sharp极大函数、几何极大函数和粗糙极大函数
IF 1 4区 数学
Mathematical Inequalities & Applications Pub Date : 2020-10-01 DOI: 10.7153/mia-2020-23-108
T. Yee, K. Cheung, K. Ho, Chun Kit Anthony Suen
{"title":"Local sharp maximal functions, geometrical maximal functions and rough maximal functions on local Morrey spaces with variable exponents","authors":"T. Yee, K. Cheung, K. Ho, Chun Kit Anthony Suen","doi":"10.7153/mia-2020-23-108","DOIUrl":"https://doi.org/10.7153/mia-2020-23-108","url":null,"abstract":"We study the local Morrey spaces with variable exponents. We show that the local block space with variable exponents are pre-duals of the local Morrey spaces with variable exponents. Using this duality, we establish the extrapolation theory for the local Morrey spaces with variable exponents. The extrapolation theory gives the mapping properties for the local sharp maximal functions, the geometric maximal functions and the rough maximal function on the local Morrey spaces with variable exponents. Mathematics subject classification (2010): 42B20, 42B35, 46E30.","PeriodicalId":49868,"journal":{"name":"Mathematical Inequalities & Applications","volume":" ","pages":""},"PeriodicalIF":1.0,"publicationDate":"2020-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41623709","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
Operator inequalities and gyrolines of the weighted geometric means 算子不等式与加权几何平均的回旋线
IF 1 4区 数学
Mathematical Inequalities & Applications Pub Date : 2020-09-22 DOI: 10.7153/MIA-2021-24-34
Sejong Kim
{"title":"Operator inequalities and gyrolines of the weighted geometric means","authors":"Sejong Kim","doi":"10.7153/MIA-2021-24-34","DOIUrl":"https://doi.org/10.7153/MIA-2021-24-34","url":null,"abstract":"We consider in this paper two different types of the weighted geometric means of positive definite operators. We show the component-wise bijection of these geometric means and give a geometric property of the spectral geometric mean as a metric midpoint. Moreover, several interesting inequalities related with the geometric means of positive definite operators will be shown. We also see the meaning of weighted geometric means in the gyrogroup structure with finite dimension and find the formulas of weighted geometric means of 2-by-2 positive definite matrices and density matrices.","PeriodicalId":49868,"journal":{"name":"Mathematical Inequalities & Applications","volume":" ","pages":""},"PeriodicalIF":1.0,"publicationDate":"2020-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44996970","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: 11
Matrix rearrangement inequalities revisited 矩阵重排不等式
IF 1 4区 数学
Mathematical Inequalities & Applications Pub Date : 2020-09-08 DOI: 10.7153/mia-2021-24-30
Victoria Chayes
{"title":"Matrix rearrangement inequalities revisited","authors":"Victoria Chayes","doi":"10.7153/mia-2021-24-30","DOIUrl":"https://doi.org/10.7153/mia-2021-24-30","url":null,"abstract":"Let $||X||_p=text{Tr}[(X^ast X)^{p/2}]^{1/p}$ denote the $p$-Schatten norm of a matrix $Xin M_{ntimes n}(mathbb{C})$, and $sigma(X)$ the singular values with $uparrow$ $downarrow$ indicating its increasing or decreasing rearrangements. We wish to examine inequalities between $||A+B||_p^p+||A-B||_p^p$, $||sigma_downarrow(A)+sigma_downarrow(B)||_p^p+||sigma_downarrow(A)-sigma_downarrow(B)||_p^p$, and $||sigma_uparrow(A)+sigma_downarrow(B)||_p^p+||sigma_uparrow(A)-sigma_downarrow(B)||_p^p$ for various values of $1leq p<infty$. It was conjectured in [5] that a universal inequality $||sigma_downarrow(A)+sigma_downarrow(B)||_p^p+||sigma_downarrow(A)-sigma_downarrow(B)||_p^pleq ||A+B||_p^p+||A-B||_p^p leq ||sigma_uparrow(A)+sigma_downarrow(B)||_p^p+||sigma_uparrow(A)-sigma_downarrow(B)||_p^p$ might hold for $1leq pleq 2$ and reverse at $pgeq 2$, potentially providing a stronger inequality to the generalization of Hanner's Inequality to complex matrices $||A+B||_p^p+||A-B||_p^pgeq (||A||_p+||B||_p)^p+|||A||_p-||B||_p|^p$. We extend some of the cases in which the inequalities of [5] hold, but offer counterexamples to any general rearrangement inequality holding. We simplify the original proofs of [5] with the technique of majorization. This also allows us to characterize the equality cases of all of the inequalities considered. We also address the commuting, unitary, and ${A,B}=0$ cases directly, and expand on the role of the anticommutator. In doing so, we extend Hanner's Inequality for complex matrices to the ${A,B}=0$ case for all ranges of $p$.","PeriodicalId":49868,"journal":{"name":"Mathematical Inequalities & Applications","volume":" ","pages":""},"PeriodicalIF":1.0,"publicationDate":"2020-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47371089","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: 6
Characterization of approximately monotone and approximately Hölder functions 近似单调和近似Hölder函数的刻画
IF 1 4区 数学
Mathematical Inequalities & Applications Pub Date : 2020-07-14 DOI: 10.7153/MIA-2021-24-18
A. Goswami, Zsolt P'ales
{"title":"Characterization of approximately monotone and approximately Hölder functions","authors":"A. Goswami, Zsolt P'ales","doi":"10.7153/MIA-2021-24-18","DOIUrl":"https://doi.org/10.7153/MIA-2021-24-18","url":null,"abstract":"A real valued function $f$ defined on a real open interval $I$ is called $Phi$-monotone if, for all $x,yin I$ with $xleq y$ it satisfies $$ \u0000f(x)leq f(y)+Phi(y-x), $$ where $Phi:[0,ell(I)[,tomathbb{R}_+$ is a given nonnegative error function, where $ell(I)$ denotes the length of the interval $I$. If $f$ and $-f$ are simultaneously $Phi$-monotone, then $f$ is said to be a $Phi$-Holder function. In the main results of the paper, using the notions of upper and lower interpolations, we establish a characterization for both classes of functions. This allows one to construct $Phi$-monotone and $Phi$-Holder functions from elementary ones, which could be termed the building blocks for those classes. In the second part, we deduce Ostrowski- and Hermite--Hadamard-type inequalities from the $Phi$-monotonicity and $Phi$-Holder properties, and then we verify the sharpness of these implications. We also establish implications in the reversed direction.","PeriodicalId":49868,"journal":{"name":"Mathematical Inequalities & Applications","volume":" ","pages":""},"PeriodicalIF":1.0,"publicationDate":"2020-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48424983","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
Inequalities from Lorentz-Finsler norms Lorentz-Finsler范数中的不等式
IF 1 4区 数学
Mathematical Inequalities & Applications Pub Date : 2020-06-18 DOI: 10.7153/mia-2021-24-26
N. Minculete, C. Pfeifer, N. Voicu
{"title":"Inequalities from Lorentz-Finsler norms","authors":"N. Minculete, C. Pfeifer, N. Voicu","doi":"10.7153/mia-2021-24-26","DOIUrl":"https://doi.org/10.7153/mia-2021-24-26","url":null,"abstract":"We show that Lorentz-Finsler geometry offers a powerful tool in obtaining inequalities. With this aim, we first point out that a series of famous inequalities such as: the (weighted) arithmetic-geometric mean inequality, Acz'el's, Popoviciu's and Bellman's inequalities, are all particular cases of a reverse Cauchy-Schwarz, respectively, of a reverse triangle inequality holding in Lorentz-Finsler geometry. Then, we use the same method to prove some completely new inequalities, including two refinements of Acz'el's inequality.","PeriodicalId":49868,"journal":{"name":"Mathematical Inequalities & Applications","volume":" ","pages":""},"PeriodicalIF":1.0,"publicationDate":"2020-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45176203","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
Mean-type mappings and invariance principle 平均类型映射和不变性原则
IF 1 4区 数学
Mathematical Inequalities & Applications Pub Date : 2020-05-21 DOI: 10.7153/mia-2021-24-15
J. Matkowski, P. Pasteczka
{"title":"Mean-type mappings and invariance principle","authors":"J. Matkowski, P. Pasteczka","doi":"10.7153/mia-2021-24-15","DOIUrl":"https://doi.org/10.7153/mia-2021-24-15","url":null,"abstract":"In the finite dimensional case, mean-type mappings, their invariant means, relations between the uniqueness of invariant means and convergence of orbits of the mapping, are considered. In particular it is shown, that the uniqueness of an invariance mean implies the convergence of all orbits. A strongly irregular mean-type mapping is constructed and its unique invariant mean is determined. An application in solving a functional equation is presented.","PeriodicalId":49868,"journal":{"name":"Mathematical Inequalities & Applications","volume":" ","pages":""},"PeriodicalIF":1.0,"publicationDate":"2020-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44695979","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
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