共查询到20条相似文献,搜索用时 0 毫秒
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Mathematical Notes - 相似文献
2.
Operator-valued Fourier Multipliers on Periodic Triebel Spaces 总被引:2,自引:0,他引:2
Shang Quan BU Jin Myong KIM 《数学学报(英文版)》2005,21(5):1049-1056
We establish operator-valued Fourier multiplier theorems on periodic Triebel spaces, where the required smoothness of the multipliers depends on the indices of the Triebel spaces. This is used to give a characterization of the maximal regularity in the sense of Triebel spaces for Cauchy problems with periodic boundary conditions. 相似文献
3.
Shangquan BU 《数学年刊B辑(英文版)》2011,32(2):293-302
The author establishes operator-valued Fourier multiplier theorems on multi-dimensional Hardy spaces H
p
($
\mathbb{T}
$
\mathbb{T}
d
;X), where 1 ≤ p < ∞, d ∈ ℕ, and X is an AUMD Banach space having the property (α). The sufficient condition on the multiplier is a Marcinkiewicz type condition of order 2 using Rademacher boundedness of
sets of bounded linear operators. It is also shown that the assumption that X has the property (α) is necessary when d ≥ 2 even for scalar-valued multipliers. When the underlying Banach space does not have the property (α), a sufficient condition on the multiplier of Marcinkiewicz type of order 2 using a notion of d-Rademacher boundedness is also given. 相似文献
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5.
Ferenc Móricz 《Monatshefte für Mathematik》2006,148(1):51-59
We extend some recent results of S. A. Telyakovskii on the uniform boundedness of the partial sums of Fourier series of functions
of bounded variation to periodic functions of two variables, which are of bounded variation in the sense of Hardy. As corollaries,
we obtain the classical Parseval formula, the convergence theorem of the series involving the sine Fourier coefficients, and
a lower estimate of the best approximation by trigonometric polynomials in the metric of L in a sharpened version.
This research was supported by the Hungarian National Foundation for Scientific Research under Grants TS 044 782 and T 046
192. 相似文献
6.
Ferenc Móricz 《Monatshefte für Mathematik》2006,61(4):51-59
We extend some recent results of S. A. Telyakovskii on the uniform boundedness of the partial sums of Fourier series of functions
of bounded variation to periodic functions of two variables, which are of bounded variation in the sense of Hardy. As corollaries,
we obtain the classical Parseval formula, the convergence theorem of the series involving the sine Fourier coefficients, and
a lower estimate of the best approximation by trigonometric polynomials in the metric of L in a sharpened version. 相似文献
7.
A. A. Saakyan 《Mathematical Notes》2003,74(1-2):255-265
In this paper, we prove that for any compact set
there exists a homeomorphism of the closed interval
such that for an arbitrary function f the Fourier series of the function F(x,y) = f((x),(y)) converges uniformly on
simultaneously over rectangles, over spheres, and over triangles. 相似文献
8.
Prem Chandra 《Proceedings Mathematical Sciences》2001,111(2):203-219
In this paper, the author has investigated necessary and sufficient conditions for the absolute Euler summability of the Fourier series with miltipliers. These conditions are weaker than those obtained earlier by some workers. It is further shown that the multipliers are best possible in certain sense. 相似文献
9.
Hiro-O Kitax 《Mathematische Nachrichten》1998,193(1):57-74
Let S* (f be the majorant function of the partial sums of the trigonometric Fourier series of f. In this paper we consider the Orlicz space Lπ and give a generalization of Soria's result [S1]. Let π (t) be a concave function with some nice properties and . If there exists a positive constant a0 < 1 such that then we have . 相似文献
10.
Fred Richman 《Mathematical Logic Quarterly》2002,48(1):111-116
A very weak omniscience principle is formulated, related omniscience principlesare considered, and the theorem that a function of bounded variation is the difference of two increasing functions is shown to be equivalent to the omniscience principle WLPO. It is a so shown that an arbitrary function (not necessarily strongly extensional) with located variation on an interval is the difference of two increasing functions. 相似文献
11.
Let E be a symmetric space on [0,1]. Let (,E) be the space of measurable functions f such that fg E for every almost everywhere convergent series g=b
n
r
n E, where (r
n) are the Rademacher functions. It was shown that, for a broad class of spaces E, the space (,E) is not order isomorphic to a symmetric space, and we study the conditions under which such an isomorphism exists. We give conditions on E for (,E) to be order isomorphic to L
. This includes some classes of Lorentz and Marcinkiewicz spaces. We also study the conditions under which (,E) is order isomorphic to a symmetric space that differs from L
. The answer is positive for the Orlicz spaces E=L
q with q(t)=exp|t|q-1 and 0
相似文献
12.
本注记给出了关于在Fourier级数L~1收敛中MVBV条件不可减弱的一个猜想的肯定回答。 相似文献
13.
This article concerns the unconditional convergence a.e. of Fourier series with respect to general orthonormal systems. We find certain conditions to be satisfied by the functions in the orthonormal system so that the Fourier series of each function of finite variation unconditionally converge a.e. The results are best possible. 相似文献
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15.
Hüseyin Bor 《Proceedings Mathematical Sciences》1992,102(1):53-58
In this paper two theorems on | N,pn;δ|k summability factors, which generalize the results of Bor [4] on | N,pn|k summability factors, have been proved. 相似文献
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单调性条件在Fourier级数收敛性中的最终推广:历史、发展、应用和猜想 总被引:1,自引:0,他引:1
为了对Fourier级数进行近似计算和有效应用,必须研究其收敛性,这个课题有长久的历史,形成了数学分析中吸引包括许多著名数学家在内的学者研究的一条热烈但困难的主流.其中,在三角级数(Fourier级数)一致收敛性和平均收敛性问题中人们一直关心Fourier系数的单调递减条件最终的推广.这个开始于英国Chaundy-Jollife(1916年)和Young(1913年)的工作最近出现了突破性的进展,产生了许多完善的结果.本文将对这方面的历史、发展给出综述,并重点介绍最近的应用成果,并对以后的工作给出研究思路和线索. 相似文献
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In this paper, by establishing a result concerning the mapping properties for bi(sub)linear operators on Morrey spaces, and the weighted estimates with general weights for the bilinear Fourier multiplier, the author establishes some results concerning the behavior on the product of Morrey spaces for bilinear Fourier multiplier operator with associated multiplierσ satisfying certain Sobolev regularity. 相似文献
18.
Mathematical Notes - 相似文献
19.
In an attempt to study the scope of a theorem due to Pati, the authors have established that φ(t) logK|t∈B
u
V in (0,π)⟹ΣA
n
(x) is |C, 0,β| forβ>1, at the pointt = x. 相似文献
20.
We know that the Box dimension of f(x) ∈ C~1[0,1] is 1. In this paper, we prove that the Box dimension of continuous functions with bounded variation is still1. Furthermore, Box dimension of Weyl fractional integral of above function is also 1. 相似文献