对各类展式的误差和函数的研究从21世纪初就开始了,研究人员不断深入探讨其各种性质,如连续性、周期性、有界性、介值性等,同时给出函数图像的Hausdorff维数。在本文中,我们将探讨Hurwitz连分数的误差和函数,提出一些相关的性质,并研究...对各类展式的误差和函数的研究从21世纪初就开始了,研究人员不断深入探讨其各种性质,如连续性、周期性、有界性、介值性等,同时给出函数图像的Hausdorff维数。在本文中,我们将探讨Hurwitz连分数的误差和函数,提出一些相关的性质,并研究其图像。The study of error-sum functions of expansions has been ongoing since the beginning of the 21st century, and researchers have been delving into various properties such as continuity, periodicity, boundedness, median, etc., along with giving the Hausdorff dimension of the graphs of the functions. In this paper, we will explore the error-sum function of Hurwitz continued fractions, present some related properties, and study their graphs.展开更多
LetΩbe homogeneous of degree zero,integrable on S^(d−1) and have vanishing moment of order one,a be a function on R^(d) such that ∇a∈L^(∞)(R^(d)).Let T*_(Ω,a) be the maximaloperator associated with the d-dimensional...LetΩbe homogeneous of degree zero,integrable on S^(d−1) and have vanishing moment of order one,a be a function on R^(d) such that ∇a∈L^(∞)(R^(d)).Let T*_(Ω,a) be the maximaloperator associated with the d-dimensional Calder´on commutator defined by T*_(Ωa)f(x):=sup_(ε>0)|∫_(|x-y|>ε)^Ω(x-y)/|x-y|^(d+1)(a(x)-a(y))f(y)dy.In this paper,the authors establish bilinear sparse domination for T*_(Ω,a) under the assumption Ω∈L∞(Sd−1).As applications,some quantitative weighted bounds for T*_(Ω,a) are obtained.展开更多
We give a new result on the construction of K-frame generators for unitary systems by using the pseudo-inverses of involved operators,which provides an improvement to one known result on this topic.We also introduce t...We give a new result on the construction of K-frame generators for unitary systems by using the pseudo-inverses of involved operators,which provides an improvement to one known result on this topic.We also introduce the concept of K-woven generators for unitary systems,by means of which we investigate the weaving properties of K-frame generators for unitary systems.展开更多
利用Hardy-Littlewood极大算子的加权有界性和Sharp极大函数的点态估计等工具,给出RD(reverse doubling)-空间上多线性强奇异Calderón-Zygmund算子及其与BMO(bounded mean oscillation)函数生成的多线性交换子在加权乘积Morrey空...利用Hardy-Littlewood极大算子的加权有界性和Sharp极大函数的点态估计等工具,给出RD(reverse doubling)-空间上多线性强奇异Calderón-Zygmund算子及其与BMO(bounded mean oscillation)函数生成的多线性交换子在加权乘积Morrey空间上的有界性.展开更多
文摘对各类展式的误差和函数的研究从21世纪初就开始了,研究人员不断深入探讨其各种性质,如连续性、周期性、有界性、介值性等,同时给出函数图像的Hausdorff维数。在本文中,我们将探讨Hurwitz连分数的误差和函数,提出一些相关的性质,并研究其图像。The study of error-sum functions of expansions has been ongoing since the beginning of the 21st century, and researchers have been delving into various properties such as continuity, periodicity, boundedness, median, etc., along with giving the Hausdorff dimension of the graphs of the functions. In this paper, we will explore the error-sum function of Hurwitz continued fractions, present some related properties, and study their graphs.
文摘LetΩbe homogeneous of degree zero,integrable on S^(d−1) and have vanishing moment of order one,a be a function on R^(d) such that ∇a∈L^(∞)(R^(d)).Let T*_(Ω,a) be the maximaloperator associated with the d-dimensional Calder´on commutator defined by T*_(Ωa)f(x):=sup_(ε>0)|∫_(|x-y|>ε)^Ω(x-y)/|x-y|^(d+1)(a(x)-a(y))f(y)dy.In this paper,the authors establish bilinear sparse domination for T*_(Ω,a) under the assumption Ω∈L∞(Sd−1).As applications,some quantitative weighted bounds for T*_(Ω,a) are obtained.
基金Supported by NSFC(Nos.12361028,11761057)Science Foundation of Jiangxi Education Department(Nos.GJJ202302,GJJ202303,GJJ202319).
文摘We give a new result on the construction of K-frame generators for unitary systems by using the pseudo-inverses of involved operators,which provides an improvement to one known result on this topic.We also introduce the concept of K-woven generators for unitary systems,by means of which we investigate the weaving properties of K-frame generators for unitary systems.
文摘利用Hardy-Littlewood极大算子的加权有界性和Sharp极大函数的点态估计等工具,给出RD(reverse doubling)-空间上多线性强奇异Calderón-Zygmund算子及其与BMO(bounded mean oscillation)函数生成的多线性交换子在加权乘积Morrey空间上的有界性.
