共查询到20条相似文献,搜索用时 15 毫秒
1.
Hacer Bilgin Ellidokuzoğlu & Serkan Demiriz 《分析论及其应用》2021,37(4):557-571
Başar and Braha [1], introduced the sequence spaces $\breve{\ell}_\infty$, $\breve{c}$ and $\breve{c}_0$ of Euler-Cesáro bounded, convergent and null difference sequences and studied their some properties. Then, in [2], we introduced the sequence spaces ${[\ell_\infty]}_{e.r}, {[c]}_{e.r}$ and ${[c_0]}_{e.r}$ of Euler-Riesz bounded, convergent and null difference sequences by using the composition of the Euler mean $E_1$ and Riesz mean $R_q$ with backward difference operator $\Delta$. The main purpose of this study is to introduce the sequence space ${[\ell_p]}_{e.r}$ of Euler-Riesz $p-$absolutely convergent series, where $1 \leq p <\infty$, difference sequences by using the composition of the Euler mean $E_1$ and Riesz mean $R_q$ with backward difference operator $\Delta$. Furthermore, the inclusion $\ell_p\subset{[\ell_p]}_{e.r}$ hold, the basis of the sequence space ${[\ell_p]}_{e.r}$ is constructed and $\alpha-$, $\beta-$ and $\gamma-$duals of the space are determined. Finally, the classes of matrix transformations from the ${[\ell_p]}_{e.r}$ Euler-Riesz difference sequence space to the spaces $\ell_\infty, c$ and $c_0$ are characterized. We devote the final section of the paper to examine some geometric properties of the space ${[\ell_p]}_{e.r}$. 相似文献
2.
In the case of Ω∈ Lipγ(Sn-1)(0 γ≤ 1), we prove the boundedness of the Marcinkiewicz integral operator μΩon the variable exponent Herz-Morrey spaces. Also, we prove the boundedness of the higher order commutators μmΩ,bwith b ∈ BMO(Rn) on both variable exponent Herz spaces and Herz-Morrey spaces, and extend some known results. 相似文献
3.
Some properties of best monotone approximants in several
variables are obtained. We prove the following abstract
characterization theorem. Let $(\om, {\cal A},\mu)$ be a
measurable space and let ${\cal L}\subset{\cal A}$ be a
$\sigma$-lattice. If $f$ belongs to a Musielak–Orlicz space $L_{\varphi}(\Omega, {\cal A},\mu),$ then there exists a $\sigma$-algebra
${\cal A}_f\subset{\cal A}$
such that $g$ is a best $\varphi$-approximant to $f$ from
$L_{\varphi}({\cal L})$ iff $g$ is a best $\varphi$-approximant to $f$ from
$L_{\p}({\cal A}_f)$. The $\sigma$-algebra ${\cal A}_f$ depends only on $f$.
When $\Omega\subset\mbox{{\bf R}}^n$ and
$L_{\varphip}({\cal L})$ is the set of monotone functions in
several variables, we give sufficient conditions on the
geometry of $\Omega$ to obtain a uniqueness theorem. This result
extends and unifies previous ones. Finally, we prove a
coincidence relation between a function and its best
$\varphi$-approximant. Our main results are new, even in the
classical Lebesgue spaces $L_p$. 相似文献
4.
We prove that the natural embedding of the metric ideal space on a finite von Neumann algebra $\mathcal{M}$ into the *-algebra of measurable operators $\tilde {\mathcal {M}}$ endowed with the topology of convergence in measure is continuous. Using this fact, we prove that the topology of convergence in measure is a minimal one among all metrizable topologies consistent with the ring structure on $\tilde {\mathcal {M}}$ . 相似文献
5.
Yair Bartal Nathan Linial Manor Mendel Assaf Naor 《Discrete and Computational Geometry》2005,33(1):27-41
In this note we consider the metric Ramsey problem for the normed
spaces $\ell_p$. Namely, given some $1\le p \le \infty$ and
$\alpha \ge 1$, and an integer $n$, we ask for the largest $m$
such that every $n$-point metric space contains an $m$-point
subspace which embeds into $\ell_p$ with distortion at most $
\alpha$. In [1] it is shown that in the case of $\ell_2$,
the dependence of $m$ on $\alpha$ undergoes a phase transition at
$\alpha =2$. Here we consider this problem for other $\ell_p$, and
specifically the occurrence of a phase transition for $p\neq 2$.
It is shown that a phase transition does occur at $\alpha=2$ for every $p\in
[1,2]$. For $p > 2$ we are unable to determine the answer, but
estimates are provided for the possible location of such a phase
transition. We also study the analogous problem for isometric
embedding and show that for every $1 < p < \infty$ there are
arbitrarily large metric spaces, no four points of which embed
isometrically in $\ell_p$. 相似文献
6.
For non-Archimedean spaces X and Y, let $\mathcal{M}_\flat \left( X \right)$ , $\mathfrak{M}\left( {V \to W} \right)$ and $\mathfrak{D}_\flat \left( {X,Y} \right)$ be the ballean of X (the family of the balls in X), the space of mappings from X to Y, and the space of mappings from the ballean of X to Y, respectively. By studying explicitly the Hausdorff metric structures related to these spaces, we construct several families of new metric structures (e.g., $\hat \rho _u$ , $\hat \beta _{X,Y}^\lambda$ , $\hat \beta _{X,Y}^{ * \lambda }$ ) on the corresponding spaces, and study their convergence, structural relation, law of variation in the variable λ, including some normed algebra structure. To some extent, the class $\hat \beta _{X,Y}^\lambda$ is a counterpart of the usual Levy-Prohorov metric in the probability measure spaces, but it behaves very differently, and is interesting in itself. Moreover, when X is compact and Y = K is a complete non-Archimedean field, we construct and study a Dudly type metric of the space of K-valued measures on X. 相似文献
7.
本文的主要建立非齐性度量测度空间上双线性强奇异积分算子$\widetilde{T}$及交换子$\widetilde{T}_{b_{1},b_{2}}$在广义Morrey空间$M^{u}_{p}(\mu)$上的有界性. 在假设Lebesgue可测函数$u, u_{1}, u_{2}\in\mathbb{W}_{\tau}$, $u_{1}u_{2}=u$,且$\tau\in(0,2)$. 证明了算子$\widetilde{T}$是从乘积空间$M^{u_{1}}_{p_{1}}(\mu)\times M^{u_{2}}_{p_{2}}(\mu)$到空间$M^{u}_{p}(\mu)$有界的, 也是从乘积空间$M^{u_{1}}_{p_{1}}(\mu)\times M^{u_{2}}_{p_{2}}(\mu)$到广义弱Morrey空间$WM^{u}_{p}(\mu)$有界的,其中$\frac{1}{p}=\frac{1}{p_{1}}+\frac{1}{p_{2}}$及$1相似文献
8.
9.
In this paper, we define the Morrey spaces M_F~(p,q) (Rn) and the Campanato spaces E_F~(p,q) (R~n) associated with a family F of sections and a doubling measure μ, where F is closely related to the Monge-Amp`ere equation. Furthermore, we obtain the boundedness of the Hardy-Littlewood maximal function associated to F, Monge-Amp`ere singular integral operators and fractional integrals on M_F~(p,q)(R~n). We also prove that the Morrey spaces M_F~(p,q) (R~n)and the Campanato spaces E_F~(p,q) (R~n) are equivalent with 1 ≤ q ≤ p ∞. 相似文献
10.
Thomas Kalmes 《Results in Mathematics》2003,43(3-4):278-283
In this note we investigate spaces of the type $ L_{\varepsilon}^{p}(\mu)=\lbrace f\in L^{p}(\mu);{\rm supp}f\in \varepsilon \rbrace $ where ε is an ideal of “small” measurable sets with certain properties. Typically, these spaces endowed with the p-norm are not complete and thus, classical Banach space theory cannot be used.However, we prove that for good ideals ε the normed space $L_\varepsilon ^{p}(\mu)$ is ultrabornological and hence barrelled and therefore many theorems of functional analysis like the closed graph theorem or the uniform boundedness principle are indeed applicable. 相似文献
11.
Some new sequence spaces derived by The composition of binomial matrix and double band matrix 下载免费PDF全文
Abdulcabbar Sonmez 《Journal of Applied Analysis & Computation》2019,9(1):231-244
In this paper, we construct three new sequence spaces $b^{{r,s}}_{0}(G)$, $b^{{r,s}}_{c}(G)$ and $b^{{r,s}}_{\infty}(G)$ and mention some inclusion relations, where $G$ is generalized difference matrix. Moreover, we give Schauder basis of the spaces $b^{{r,s}}_{0}(G)$ and $b^{{r,s}}_{c}(G)$. Afterward, we determine $\alpha-$, $\beta-$ and $\gamma-$duals of those spaces. Finally, we characterize some matrix classes related to the space $b^{{r,s}}_{c}(G)$. 相似文献
12.
《Optimization》2012,61(1):31-45
In this paper, we define the Mosco convergence and Kuratowski-Painleve (P.K.) convergence for set-valued mapping sequence F n . Under some conditions, we derive the following result If a set-valued mapping sequence F n , which are nonempty, compact valued, upper semicontinuous and uniformly bounded below, Mosco (or P.K.) converges to a set-valued mapping F , which is upper semicontinuous, nonempty, compact valued, then Q l >0, u >0, $\varepsilon / \lambda - {\rm ext}\, F := \{ \bar x \in X : (F(x) - \bar y + \varepsilon / \lambda \Vert x - \bar x \Vert e)$ 相似文献
13.
On Some Applications of Geometry of Banach Spaces and Some New Results Related to the Fixed Point Theory in Orlicz Sequence Spaces 下载免费PDF全文
Yunan Cui Henryk Hudzik Radosław Kaczmarek Haifeng Ma Yuwen Wang & Meiling Zhang 《数学研究》2016,49(4):325-378
We present some applications of the geometry of Banach spaces in the approximation
theory and in the theory of generalized inverses. We also give some new
results, on Orlicz sequence spaces, related to the fixed point theory. After a short introduction, in Section 2 we
consider the best approximation projection from a Banach space $X$ onto its non-empty
subset and proximinality of the subspaces of order continuous elements in various
classes of Köthe spaces. We present formulas for the distance to these subspaces of
the elements from the outside of them. In Section 3 we recall some results and definitions
concerning generalized inverses of operators (metric generalized inverses and
Moore-Penrose generalized inverses). We also recall some results on the perturbation
analysis of generalized inverses in Banach spaces. The last part of this section concerns
generalized inverses of multivalued linear operators (their definitions and representations).
The last section starts with a formula for modulus of nearly uniform
smoothness of Orlicz sequence spaces $\ell^\Phi$equipped with the Amemiya-Orlicz norm.
From this result a criterion for nearly uniform smoothness of these spaces is deduced.
A formula for the Domínguez-Benavides coefficient $R(a,l_\Phi)$ is also presented, whence
a sufficient condition for the weak fixed point property of the space $\ell^\Phi$is obtained. 相似文献
14.
Antal Járai 《Aequationes Mathematicae》2003,65(3):236-266
Summary. We prove that - under certain conditions - measurable solutions $f$ of the functional equation $f(x)=h(x,y,f(g_{1}(x,y)),\ldots,f(g_{n}(x,y))),\quad(x,y)\in D \subset \mathbb{R}^{s} \times \mathbb{R}^{l}$ are continuous, even if $1\le l\le s$. As a tool we introduce new classes of functions which - roughly speaking - interpolate between continuous and Lebesgue measurable functions. Connection between these classes are also investigated. 相似文献
15.
Nicola Gigli 《Calculus of Variations and Partial Differential Equations》2010,39(1-2):101-120
We prove existence and uniqueness of the gradient flow of the Entropy functional under the only assumption that the functional is λ-geodesically convex for some ${\lambda\in\mathbb {R}}$ . Also, we prove a general stability result for gradient flows of geodesically convex functionals which Γ?converge to some limit functional. The stability result applies directly to the case of the Entropy functionals on compact spaces. 相似文献
16.
In this paper, we mainly study an inverse source problem of time fractional diffusion equation in a bounded domain with an over-specified terminal condition at a fixed time. A novel regularization method, which we call the exponential Tikhonov regularization method with a parameter $\gamma$, is proposed to solve the inverse source problem, and the corresponding convergence analysis is given under a-priori and a-posteriori regularization parameter choice rules. When $\gamma$ is less than or equal to zero, the optimal convergence rate can be achieved and it is independent of the value of $\gamma$. However, when $\gamma$ is greater than zero, the optimal convergence rate depends on the value of $\gamma$ which is related to the regularity of the unknown source. Finally, numerical experiments are conducted for showing the effectiveness of the proposed exponential regularization method. 相似文献
17.
Assume that we want to recover $f : \Omega \to {\bf C}$ in the
$L_r$-quasi-norm ($0 < r \le \infty$) by a linear sampling method
$$
S_n f = \sum_{j=1}^n f(x^j) h_j ,
$$
where $h_j \in L_r(\Omega )$ and $x^j \in \Omega$
and $\Omega \subset {\bf R}^d$ is an arbitrary bounded Lipschitz domain.
We assume that $f$ is from the unit ball of
a Besov space $B^s_{pq} (\Omega)$ or of a
Triebel--Lizorkin space $F^s_{pq} (\Omega)$ with
parameters such that the space is compactly embedded
into $C(\overline{\Omega})$. We prove that the optimal rate
of convergence of linear sampling methods is
$$
n^{ -{s}/{d} + ({1}/{p}-{1}/{r})_+} ,
$$
nonlinear methods do not yield a better rate.
To prove this we use a result from Wendland (2001) as well
as results concerning the spaces $B^s_{pq} (\Omega) $ and $F^s_{pq}(\Omega)$.
Actually, it is another aim of this paper to complement the
existing literature about the function spaces $B^s_{pq} (\Omega)$ and $F^s_{pq}
(\Omega)$ for bounded Lipschitz domains $\Omega \subset {\bf R}^d$.
In this sense, the paper is also a continuation of a paper by Triebel (2002). 相似文献
18.
作者引入了非齐型空间上的弱Herz空间,并建立了一类次线性算子在这些空间中的弱型估计. 作为应用, 证明了由Calder\'on-Zygmund算子和$\os$函数生成的交换子在弱Herz空间中的弱型估计,其中$r\ge1$. 并且Orlicz空间$\os$当$r=1$时即为$\rb$空间;当$r>1$时为$\rb$的子空间. 相似文献
19.
本文讨论齐型空间上$L^1$ 与{\rm BMO}的内插空间, 得到下列结果:对于本文讨论齐型空间上$L^1$ 与{\rm BMO}的内插空间, 得到下列结果:对于本文讨论齐型空间上$L^1$ 与{\rm BMO}的内插空间, 得到下列结果:对于摘要:本文讨论齐型空间上L^1与BMO的内插空间,得到下列结果:对于0〈θ〈1,1≤q≤∞,有(L^1,BMO)θ,q=Lpq,其中θ=1-1/p。 相似文献
20.
卷积型Calder\'{o}n-Zygmund算子的新算法 总被引:1,自引:0,他引:1
Beylkin-Coifman-Rokhlin
(B-C-R)算法表明算子通常可用$2n$维小波来分析, 而本文用
基于$n$维小波来引入一种新方法考虑卷积型 Calder\'{o}n-Zygmund
(C-Z)算子. 利用此方法来研究算子的逼近, 此逼近算法不仅比 B-C-R
算法简单而且有更快的逼近速度. 还证明了 H\"{o}rmander
条件能够保证算子在 Besov 空间$\dot{B}_p^{0,q}\ (1\leq p,\, q
\leq\infty)$ 和 Triebel--Lizorkin 空间$\dot{F}_p^{0,q}(1
相似文献