共查询到20条相似文献,搜索用时 15 毫秒
1.
本文研究了一类次线性算子及其交换子在齐型空间上的弱有界性的问题.利用齐型空间的基本性质以及给出的一类次线性算子及其分别与BMO函数,Lipschitz函数生成的交换子在L~p(X)上的弱有界性,证明了其在齐型空间上Morrey-Herz空间中的弱有界性.推广了该类算子在Morrey-Herz空间中的强有界性这一结果. 相似文献
2.
A normed space is paracomplete if it admits a new norm, stronger than the initial one, that makes it complete. Here we give
a characterization of paracomplete normed spaces. As a consequence, we show that operators on paracomplete spaces have compact
spectrum in the algebra of all operators, and that the class of paracomplete spaces is not stable under ℓ2-sums. Moreover, we give characterizations for the closed Fredholm operators on paracomplete spaces and for the almost semi-Fredholm
operators of Harte on normed spaces. 相似文献
3.
Olivia Constantin 《Journal of Mathematical Analysis and Applications》2010,365(2):668-682
We prove Carleson-type embedding theorems for weighted Bergman spaces with Békollé weights. We use this to study properties of Toeplitz-type operators, integration operators and composition operators acting on such spaces. In particular, we investigate the membership of these operators to Schatten class ideals. 相似文献
4.
研究次范整线性空间上的可加奇性算子理论.引进可加奇性算子的三种不同的次范数和拟次范数,利用它们刻画可加奇性算子的三种有界性:有界、局部有界和球有界,深入讨论这三种有界性之间的关系,以及它们与连续性的关系.同时,还进一步研究次范整线性空间上连续可加奇性算子族的共鸣定理. 相似文献
5.
Wen-Chi Kuo 《Journal of Mathematical Analysis and Applications》2005,303(2):509-521
Conditional expectations operators acting on Riesz spaces are shown to commute with a class of principal band projections. Using the above commutation property, conditional expectation operators on Riesz spaces are shown to be averaging operators. Here the theory of f-algebras is used when defining multiplication on the Riesz spaces. This leads to the extension of these conditional expectation operators to their so-called natural domains, i.e., maximal domains for which the operators are both averaging operators and conditional expectations. The natural domain is in many aspects analogous to L1. 相似文献
6.
Justin Feuto 《Journal of Fourier Analysis and Applications》2014,20(4):896-909
We prove that Calderón-Zygmund operators, Marcinkiewicz operators, maximal operators associated to Bochner-Riesz operators, operators with rough kernel as well as commutators associated to these operators which are known to be bounded on weighted Morrey spaces under appropriate conditions, are bounded on a wide family of function spaces. 相似文献
7.
Ioana Ghenciu 《Monatshefte für Mathematik》2020,191(4):719-733
In this paper we introduce p-Dunford–Pettis completely continuous operators and study Banach spaces with the wp-Dunford–Pettis relative compact property (wp-DPrcP). We study the behaviour of p-Dunford–Pettis completely operators on spaces with this property. We give sufficient conditions for spaces of operators to have the wp-DPrcP. 相似文献
8.
某些算子和交换子在非齐型空间上的Morrey-Herz空间中的有界性 总被引:2,自引:0,他引:2
引入了非齐型空间上的齐次Morrey-Herz 空间和弱齐次Morrey-Herz空间并建立了Hardy-Littlewood极大算子,Calder\'on-Zygmund算子和分数次积分算子在齐次Morrey-Herz空间中的有界性以及在弱齐次Morrey-Herz空间中的弱型估计. 此外,还证明了$\rb$函数与Calder\'on-Zygmund算子或分数次积分算子生成的多线性交换子以及与Hardy-Littlewood极大算子相关的极大交换子在齐次Morrey-Herz空间中的有界性. 相似文献
9.
Egon Scheffold 《Acta Mathematica Hungarica》2005,108(1-2):13-23
Summary Certain bounded linear operators from Hilbert spaces H into function spaces C(X) are approximated by operators of finite rank with the aid of orthogonal projections. As examples for such operators we present special integral operators and linear partial differential operators. As application we consider a collocation method. 相似文献
10.
Nina Zorboska 《Proceedings of the American Mathematical Society》1998,126(7):2013-2023
We characterize bounded and compact composition operators on weighted Dirichlet spaces. The method involves integral averages of the determining function for the operator, and the connection between composition operators on Dirichlet spaces and Toeplitz operators on Bergman spaces. We also present several examples and counter-examples that point out the borderlines of the result and its connections to other themes.
11.
We study the boundedness of Toeplitz operators on Segal–Bargmann spaces in various contexts. Using Gutzmer’s formula as the
main tool we identify symbols for which the Toeplitz operators correspond to Fourier multipliers on the underlying groups.
The spaces considered include Fock spaces, Hermite and twisted Bergman spaces and Segal–Bargmann spaces associated to Riemannian
symmetric spaces of compact type. 相似文献
12.
S. Albeverio A. Yu. Khrennikov V.M. Shelkovich 《Journal of Fourier Analysis and Applications》2006,12(4):393-425
In this article the p-adic Lizorkin spaces of test functions and distributions are introduced. Multi-dimensional Vladimirov’s
and Taibleson’s fractional operators, and a class of p-adic pseudo-differential operators are studied on these spaces. Since
the p-adic Lizorkin spaces are invariant under these operators, they can play a key role in considerations related to fractional
operator problems. Solutions of pseudo-differential equations are also constructed. Some problems of spectral analysis of
pseudo-differential operators are studied. p-Adic multidimensional Tauberian theorems connected with these pseudo-differential
operators for the Lizorkin distributions are proved. 相似文献
13.
Kevin Beanland 《Israel Journal of Mathematics》2011,182(1):47-59
Using the notion of S
ξ
-strictly singular operators introduced by Androulakis, Dodos, Sirotkin and Troitsky, we define an ordinal index on the subspace
of strictly singular operators between two separable Banach spaces. In our main result, we provide a sufficient condition
implying that this index is bounded by ω
1. In particular, we apply this result to study operators on totally incomparable spaces, hereditarily indecomposable spaces
and spaces with few operators. 相似文献
14.
We study some categorical aspects of quasi-uniform spaces (mainly separation and epimorphisms) via closure operators in the sense of Dikranjan, Giuli, and Tholen. In order to exploit better the corresponding properties known for topological spaces we describe the behaviour of closure operators under the lifting along the forgetful functor T from quasi-uniform spaces to topological spaces. By means of appropriate closure operators we compute the epimorphisms of many categories of quasi-uniform spaces defined by means of separation axioms and study the preservation (reflection) of epimorphisms under the functor T. 相似文献
15.
This paper discusses the special properties of the spectrum of linear operators (in particular, bounded linear operators) on quotient indecomposable Banach spaces; shows that in such spaces generators of Co-groups are always bounded linear operators, and that generators of Co-semigroups satisfy the spectral mapping theorem; and gives an example to show that the generators of Co-semigroups in quotient indecomposable spaces are not necessarily bounded. 相似文献
16.
《偏微分方程通讯》2013,38(5-6):1161-1181
Abstract A symbolic calculus for the transposes of a class of bilinear pseudodifferential operators is developed. The calculus is used to obtain boundedness results on products of Lebesgue spaces. A larger class of pseudodifferential operators that does not admit a calculus is also considered. Such a class is the bilinear analog of the so-called exotic class of linear pseudodifferential operators and fail to produce bounded operators on products of Lebesgue spaces. Nevertheless, the operators are shown to be bounded on products of Sobolev spaces with positive smoothness, generalizing the Leibniz rule estimates for products of functions. 相似文献
17.
Weighted composition operators have been related to products of composition operators and their adjoints and to isometries of Hardy spaces. In this paper, Hermitian weighted composition operators on weighted Hardy spaces of the unit disk are studied. In particular, necessary conditions are provided for a weighted composition operator to be Hermitian on such spaces. On weighted Hardy spaces for which the kernel functions are ${(1 - \overline{w}z)^{-\kappa}}$ for κ ≥ 1, including the standard weight Bergman spaces, the Hermitian weighted composition operators are explicitly identified and their spectra and spectral decompositions are described. Some of these Hermitian operators are part of a family of closely related normal weighted composition operators. In addition, as a consequence of the properties of weighted composition operators, we compute the extremal functions for the subspaces associated with the usual atomic inner functions for these weighted Bergman spaces and we also get explicit formulas for the projections of the kernel functions on these subspaces. 相似文献
18.
We define Toeplitz operators on all Dirichlet spaces on the unit ball of
and develop their basic properties. We characterize bounded, compact, and Schatten-class Toeplitz operators with positive
symbols in terms of Carleson measures and Berezin transforms. Our results naturally extend those known for weighted Bergman
spaces, a special case applies to the Arveson space, and we recover the classical Hardy-space Toeplitz operators in a limiting
case; thus we unify the theory of Toeplitz operators on all these spaces. We apply our operators to a characterization of
bounded, compact, and Schatten-class weighted composition operators on weighted Bergman spaces of the ball. We lastly investigate
some connections between Toeplitz and shift operators.
The research of the second author is partially supported by a Fulbright grant. 相似文献
19.
Tepper L. Gill Sudeshna Basu Woodford W. Zachary V. Steadman 《Proceedings of the American Mathematical Society》2004,132(5):1429-1434
In this paper we show that a result of Gross and Kuelbs, used to study Gaussian measures on Banach spaces, makes it possible to construct an adjoint for operators on separable Banach spaces. This result is used to extend well-known theorems of von Neumann and Lax. We also partially solve an open problem on the existence of a Markushevich basis with unit norm and prove that all closed densely defined linear operators on a separable Banach space can be approximated by bounded operators. This last result extends a theorem of Kaufman for Hilbert spaces and allows us to define a new metric for closed densely defined linear operators on Banach spaces. As an application, we obtain a generalization of the Yosida approximator for semigroups of operators.
20.
Lanzhe Liu 《Proceedings Mathematical Sciences》2004,114(3):235-251
In this paper, the boundedness properties for some multilinear operators related to certain integral operators from Lebesgue
spaces to Orlicz spaces are obtained. The operators include Calderón—Zygmund singular integral operator, fractional integral
operator, Littlewood—Paley operator and Marcinkiewicz operator. 相似文献