We show that, given a tempered distribution T whose Fourier transform is a function of polynomial growth and a point x in Rn at which T has the value c （in the sense of Lojasiewicz）, the Fourier integral of T at x i...We show that, given a tempered distribution T whose Fourier transform is a function of polynomial growth and a point x in Rn at which T has the value c （in the sense of Lojasiewicz）, the Fourier integral of T at x is summable in Bochner-Riesz means to c.展开更多
We characterize a class of piecewise linear spectral sequences. Associated with the spectral sequence, we construct an orthonormal exponential bases for L2（[0,1）d）, which are called generalized Fourier bases. Moreo...We characterize a class of piecewise linear spectral sequences. Associated with the spectral sequence, we construct an orthonormal exponential bases for L2（[0,1）d）, which are called generalized Fourier bases. Moreover, we investigate the convergence of Bochner-Riesz means of the generalized Fourier series.展开更多
The aim of this paper is to state some conjectures and problems on Bochner-Riesz means in multiple Fourier series and integrals. The progress on these conjectures and problems are also mentioned.
设f∈L^p(R^n),1≤p≤2(n+1)/n+3,以及δ>n/p-(n+1)/2.本文证明了f在R^n上的Bochner-Riesz平均σR(f;x)满足关系式其中权函数w满足条件w(u)≥0以及1≤1/t integral from 0 to t(w(u)du≤C)(C为一绝对常数)。结论对周期情形也成立。
Ⅰ. INTRODUCTION Let ∑<sub>n</sub>= {u∈R<sup>n+1</sup>; |u|=1} be the unit sphere in （n+1）dimensional Euclidean space. For any functionf on ∑<sub>n</sub>, we associate its expa...Ⅰ. INTRODUCTION Let ∑<sub>n</sub>= {u∈R<sup>n+1</sup>; |u|=1} be the unit sphere in （n+1）dimensional Euclidean space. For any functionf on ∑<sub>n</sub>, we associate its expansion in spherical harmonics:展开更多
We prove equiconvergence of the Bochner-Riesz means of the Fourier series and integral of distributions with compact support from the Liouville spaces.
Let Kn be the n -dimensional vector space over a local field K . Two maximal multiplier theorems on Lp(Kn) are proved for certain multiplier operator sequences associated with regularization and dilation respectively ...Let Kn be the n -dimensional vector space over a local field K . Two maximal multiplier theorems on Lp(Kn) are proved for certain multiplier operator sequences associated with regularization and dilation respectively Consequently the a. e. convergence of such multiplier operator sequences is obtained This sharpens Taibleson’s main result and applies to several important singular integral operators on Kn.展开更多
In this paper we consider lim _(R-) B_R^(f,x_0), in one case that f_x_0 (t) is a ABMV function on [0, ∞], and in another case that f∈L_(m-1)~1(R~) and x^k/~kf∈BV(R) when |k| = m-1 and f(x) = 0 when |x -x_0|<δ f...In this paper we consider lim _(R-) B_R^(f,x_0), in one case that f_x_0 (t) is a ABMV function on [0, ∞], and in another case that f∈L_(m-1)~1(R~) and x^k/~kf∈BV(R) when |k| = m-1 and f(x) = 0 when |x -x_0|<δ for some δ>0. Our theormes improve the results of Pan Wenjie ([1]).展开更多
We establish Littlewood-Paley charaterizations of Triebel-Lizorkin spaces and Besov spaces in Euclidean spaces using several square functions defined via the spherical average,the ball average,the Bochner-Riesz means ...We establish Littlewood-Paley charaterizations of Triebel-Lizorkin spaces and Besov spaces in Euclidean spaces using several square functions defined via the spherical average,the ball average,the Bochner-Riesz means and some other well-known operators.We provide a simple proof so that we are able to extend and improve many results published in recent papers.展开更多
文摘We show that, given a tempered distribution T whose Fourier transform is a function of polynomial growth and a point x in Rn at which T has the value c （in the sense of Lojasiewicz）, the Fourier integral of T at x is summable in Bochner-Riesz means to c.
基金supported by Science and Technology Research Project of Jilin Provincial Department of Education of China (Grant No. 2011175)supported by National Natural Science Foundation of China (Grant Nos. 11071250 and 11126149),supported by National Natural Science Foundation of China (Grant Nos. 11071250 and 11271162)Guangdong Provincial Government of China through the "Computational Science Innovative Research Team" program
文摘We characterize a class of piecewise linear spectral sequences. Associated with the spectral sequence, we construct an orthonormal exponential bases for L2（[0,1）d）, which are called generalized Fourier bases. Moreover, we investigate the convergence of Bochner-Riesz means of the generalized Fourier series.
文摘The aim of this paper is to state some conjectures and problems on Bochner-Riesz means in multiple Fourier series and integrals. The progress on these conjectures and problems are also mentioned.
文摘设f∈L^p(R^n),1≤p≤2(n+1)/n+3,以及δ>n/p-(n+1)/2.本文证明了f在R^n上的Bochner-Riesz平均σR(f;x)满足关系式其中权函数w满足条件w(u)≥0以及1≤1/t integral from 0 to t(w(u)du≤C)(C为一绝对常数)。结论对周期情形也成立。
基金Project supported by the National Natural Science Foundation of China
文摘Ⅰ. INTRODUCTION Let ∑<sub>n</sub>= {u∈R<sup>n+1</sup>; |u|=1} be the unit sphere in （n+1）dimensional Euclidean space. For any functionf on ∑<sub>n</sub>, we associate its expansion in spherical harmonics:
文摘We prove equiconvergence of the Bochner-Riesz means of the Fourier series and integral of distributions with compact support from the Liouville spaces.
基金Project supported partially by the National Natural Science Foundation of China.
文摘Let Kn be the n -dimensional vector space over a local field K . Two maximal multiplier theorems on Lp(Kn) are proved for certain multiplier operator sequences associated with regularization and dilation respectively Consequently the a. e. convergence of such multiplier operator sequences is obtained This sharpens Taibleson’s main result and applies to several important singular integral operators on Kn.
文摘In this paper we consider lim _(R-) B_R^(f,x_0), in one case that f_x_0 (t) is a ABMV function on [0, ∞], and in another case that f∈L_(m-1)~1(R~) and x^k/~kf∈BV(R) when |k| = m-1 and f(x) = 0 when |x -x_0|<δ for some δ>0. Our theormes improve the results of Pan Wenjie ([1]).
基金supported by National Natural Science Foundation of China(Grant Nos.11971295,11871108 and 11871436)Natural Science Foundation of Shanghai(No.19ZR1417600).
文摘We establish Littlewood-Paley charaterizations of Triebel-Lizorkin spaces and Besov spaces in Euclidean spaces using several square functions defined via the spherical average,the ball average,the Bochner-Riesz means and some other well-known operators.We provide a simple proof so that we are able to extend and improve many results published in recent papers.
