共查询到20条相似文献,搜索用时 11 毫秒
1.
H. Kita 《Acta Mathematica Hungarica》1997,77(1-2):1-13
2.
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
3.
In the present paper, we give necessary and sufficient conditions for the boundedness of commutators of fractional maximal operator on Orlicz spaces. The main advance in comparison with the existing results is that we manage to obtain conditions for the boundedness not in integral terms but in less restrictive terms of supremal operators. 相似文献
4.
在赋Orlicz范数的Orlicz空间中,给出最佳逼近算子单调性的一个充分条件和最佳逼近元存在定理. 相似文献
5.
H. Kita 《Mathematische Nachrichten》1997,183(1):135-155
Let Φ(t) and Ψ(t) be the functions having the following representations Φ(t) = ∫a(s)ds and Ψ(t) = ∫b(s) ds, where a(s) is a positive continuous function such that ∫a(s)/s ds = + ∞ and b(s) is an increasing function such that lims→ ∞ b(s) = + ∞. Then the following statements for the Hardy - Littlewood maximal function M f (x) are equivalent:
- 1 (i) there exist positive constants c1 and s0 such that
- 1 (ii) there exist positive constant c2 and c3 such that
6.
7.
If
is an RUC-basis in somecouple of non-commutative L
p-spaces, then
is an RUC-basic sequence in any non-commutative Orlicz or Lorentz space which is an interpolation space for this couple. 相似文献
8.
We explore subspaces of maximal operator spaces (
submaximal spaces) and give a new characterization of such spaces. We show that the set
of n-dimensional submaximal spaces is closed in the topology of c.b. distance,
but not compact. We also investigate subspaces of MAX(L
) and prove that
any homogeneous Hilbertian subspace of MAX(L
1) is completely isomorphic
to R + C. 相似文献
9.
插值算子逼近是逼近论中一个非常有趣的问题,尤其是以一些特殊的点为结点的插值算子的逼近问题很受人们的关注.研究了以第一类Chebyshev多项式零点为插值结点的Hermite插值算子在Orlicz范数下的逼近. 相似文献
10.
In this article we consider the best polynomial approximation operator, defined in an Orlicz space L Φ(B), and its extension to L ?(B) where ? is the derivative function of Φ. A characterization of these operators and several properties are obtained. 相似文献
11.
Zhu Xuexian 《分析论及其应用》2001,17(4):65-76
Let Mg be the maximal operator defined by $$M_g f\left( x \right) = \sup \frac{{\int_a^b {f\left( y \right)g\left( y \right){\text{d}}y} }}{{\int_a^b {g\left( y \right){\text{d}}y} }}$$ , where g is a positive locally integrable function on R and the supremum is taken over all intervals [a,b] such that 0≤a≤x≤b/η(b?a), here η is a non-increasing function such that η (0) = 1 and $\mathop {{\text{lim}}}\limits_{t \to {\text{ + }}\infty } \eta \left( t \right) = 0$ η (t) = 0. This maximal function was introduced by H. Aimar and L. L. Forzani [AF]. Let Φ be an N - function such that Φ and its complementary N - function satisfy Δ2. It gives an A′Φ(g) type characterization for the pairs of weights (u,v) such that the weak type inequality $$u\left( {\left\{ {x \in {\text{R}}\left| {M_g f\left( x \right) >\lambda } \right.} \right\}} \right) \leqslant \frac{C}{{\Phi \left( \lambda \right)}}\int_{\text{R}} {\Phi \left( {\left| f \right|v} \right)} $$ holds for every f in the Orlicz space LΦ(v). And, there are no (nontrivial) weights w for which (w,w) satisfies the condition A′Φ(g). 相似文献
12.
Zhu Xuexian 《逼近论及其应用》2001,17(4):65-76
Let Mg be the maximal operator defined by
Mg f( x ) = sup\fracòab f( y )g( y )\textdy òab g( y )\textdy M_g f\left( x \right) = \sup \frac{{\int_a^b {f\left( y \right)g\left( y \right){\text{d}}y} }}{{\int_a^b {g\left( y \right){\text{d}}y} }} 相似文献
13.
14.
In this paper we pursue the study of the best approximation operator extended from L~Φ to L~φ, where φ denotes the derivative of the function Φ. We get pointwise convergence for the coefficients of the extended best approximation polynomials for a wide class of function f, closely related to the Calder′on–Zygmund class t_m~p(x) which had been introduced in 1961. We also obtain weak and strong type inequalities for a maximal operator related to the extended best polynomial approximation and a norm convergence result for the coefficients is derived. In most of these results, we have to consider Matuszewska–Orlicz indices for the function φ. 相似文献
15.
On the real line, the Dunkl operators$$D_{\nu}(f)(x):=\frac{d f(x)}{dx} + (2\nu+1) \frac{f(x) - f(-x)}{2x}, ~~ \quad\forall \, x \in \mathbb{R}, ~ \forall \, \nu \ge -\tfrac{1}{2}$$are differential-difference operators associated with the reflection group $\mathbb{Z}_2$ on $\mathbb{R}$, and on the $\mathbb{R}^d$ the Dunkl operators $\big\{D_{k,j}\big\}_{j=1}^{d}$ are the differential-difference operators associated with the reflection group $\mathbb{Z}_2^d$ on $\mathbb{R}^{d}$.In this paper, in the setting $\mathbb{R}$ we show that $b \in BMO(\mathbb{R},dm_{\nu})$ if and only if the maximal commutator $M_{b,\nu}$ is bounded on Orlicz spaces $L_{\Phi}(\mathbb{R},dm_{\nu})$. Also in the setting $\mathbb{R}^{d}$ we show that $b \in BMO(\mathbb{R}^{d},h_{k}^{2}(x) dx)$ if and only if the maximal commutator $M_{b,k}$ is bounded on Orlicz spaces $L_{\Phi}(\mathbb{R}^{d},h_{k}^{2}(x) dx)$. 相似文献
16.
The generalized maximal operator M in martingale spaces is considered. For 1 < p ≤ q < ∞, the authors give a necessary and sufficient condition on the pair ([^(m)]\hat \mu , v) for M to be a bounded operator from martingale space L
p
(v) into L
q
([^(m)]\hat \mu ) or weak-L
q
([^(m)]\hat \mu ), where [^(m)]\hat \mu is a measure on Ω × ℕ and v a weight on Ω. Moreover, the similar inequalities for usual maximal operator are discussed. 相似文献
17.
《数学的实践与认识》2013,(21)
研究了Orlicz空间中迭代Hardy-Littlewood极大函数的反加权不等式的一个等价条件,利用权函数以及分布函数的性质,结果推广了已有的关于Hardy-Littlewood极大函数的反加权不等式的结论. 相似文献
18.
Various characterizations are given of the exponential Orlicz space L and the Orlicz‐Lorentz space L. By way of application we give a simple proof of the celebrated theorem of Brézis and Wainger concerning a limiting case of a Sobolev imbedding theorem. 相似文献
19.
Let \(0\le \alpha <n\), \([b,M_{\alpha }]\) and \([b,M^{\sharp }]\) be the nonlinear commutators of the fractional maximal function \(M_{\alpha }\) and the sharp maximal function \(M^{\sharp }\) with a locally integrable function b. In this note, we give necessary and sufficient conditions for the boundedness of \([b,M_{\alpha }]\) and \([b,M^{\sharp }]\) on Orlicz spaces when the symbol b belongs to Lipschitz spaces, by which some new characterizations of non-negative Lipschitz functions (in terms of the Orlicz norm) are obtained. 相似文献
20.
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
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