共查询到20条相似文献,搜索用时 15 毫秒
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Juan F. Mena-Jurado Francisco Montiel-Aguilera 《Journal of Mathematical Analysis and Applications》2004,289(1):30-34
In this note, we characterize nice operators in a class of Banach spaces, which includes spaces and L1(μ), as those operators that preserve extreme points. 相似文献
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J.M. Calabuig E.A. Sánchez Pérez 《Journal of Mathematical Analysis and Applications》2010,364(1):88-136
In order to extend the theory of optimal domains for continuous operators on a Banach function space X(μ) over a finite measure μ, we consider operators T satisfying other type of inequalities than the one given by the continuity which occur in several well-known factorization theorems (for instance, Pisier Factorization Theorem through Lorentz spaces, pth-power factorable operators …). We prove that such a T factorizes through a space of multiplication operators which can be understood in a certain sense as the optimal domain for T. Our extended optimal domain technique does not need necessarily the equivalence between μ and the measure defined by the operator T and, by using δ-rings, μ is allowed to be infinite. Classical and new examples and applications of our results are also given, including some new results on the Hardy operator and a factorization theorem through Hilbert spaces. 相似文献
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We study the boundedness and the compactness of composition operators on some Banach function spaces such as absolutely continuous Banach function spaces on a -finite measure space, Lorentz function spaces on a -finite measure space and rearrangement invariant spaces on a resonant measure space. In addition, we study some properties of the spectra of a composition operator on the general Banach function spaces.
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Zdeněk Mihula 《Mathematische Nachrichten》2023,296(8):3492-3538
The behavior of certain weighted Hardy-type operators on rearrangement-invariant function spaces is thoroughly studied. Emphasis is put on the optimality of the obtained results. First, the optimal rearrangement-invariant function spaces guaranteeing the boundedness of the operators from/to a given rearrangement-invariant function space are described. Second, the optimal rearrangement-invariant function norms being sometimes complicated, the question of whether and how they can be simplified to more manageable expressions is addressed. Next, the relation between optimal rearrangement-invariant function spaces and interpolation spaces is investigated. Last, iterated weighted Hardy-type operators are also studied. 相似文献
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Zhijian Wu Ruhan Zhao Nina Zorboska 《Proceedings of the American Mathematical Society》2006,134(12):3531-3542
We characterize complex measures on the unit disk for which the Toeplitz operator , is bounded or compact on the Bloch type spaces .
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Let be Banach spaces and let be closed operator ideals. Let be a Banach space having the Radon-Nikodým property. The main results are as follows. If is a Hahn-Banach extension operator, then there exists a set of Hahn-Banach extension operators , , such that , where . If is an ideal in for all equivalently renormed versions of , then there exist Hahn-Banach extension operators and such that .
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In this paper, we study the matrix multiplication operators on Banach function spaces and discuss their applications in semigroups
for solving the abstract Cauchy problem. 相似文献
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Mitsuru Sugimoto Naohito Tomita 《Proceedings of the American Mathematical Society》2008,136(5):1681-1690
We prove that pseudo-differential operators with symbols in the class ( ) are not always bounded on the modulation space ().
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Bilinear operators on Herz-type Hardy spaces 总被引:4,自引:0,他引:4
Loukas Grafakos Xinwei Li Dachun Yang 《Transactions of the American Mathematical Society》1998,350(3):1249-1275
The authors prove that bilinear operators given by finite sums of products of Calderón-Zygmund operators on are bounded from into if and only if they have vanishing moments up to a certain order dictated by the target space. Here are homogeneous Herz-type Hardy spaces with and . As an application they obtain that the commutator of a Calderón-Zygmund operator with a BMO function maps a Herz space into itself.
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Lova Zakariasy 《Proceedings of the American Mathematical Society》2003,131(4):1177-1180
We show that on the harmonic Bergman spaces, the Hankel operators with nonconstant harmonic symbol cannot be of finite rank.
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Well-bounded operators on nonreflexive Banach spaces 总被引:1,自引:0,他引:1
Every well-bounded operator on a reflexive Banach space is of type (B), and hence has a nice integral representation with respect to a spectral family of projections. A longstanding open question in the theory of well-bounded operators is whether there are any nonreflexive Banach spaces with this property. In this paper we extend the known results to show that on a very large class of nonreflexive spaces, one can always find a well-bounded operator which is not of type (B). We also prove that on any Banach space, compact well-bounded operators have a simple representation as a combination of disjoint projections.
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S. Pilipovi? 《Journal of Functional Analysis》2004,208(1):194-228
The boundedness of pseudodifferential operators on modulation spaces defined by the means of almost exponential weights is studied. The results are applied to symbol class with almost exponential bounds including polynomial and ultra-polynomial symbols. The Weyl correspondence is used and it is noted that the results can be transferred to the operators with appropriate anti-Wick symbols. It is proved that a class of elliptic pseudodifferential operators can be almost diagonalized by the elements of Wilson bases, and estimates for their eigenvalues are given. Furthermore, it is shown that the same can be done by using Gabor frames. 相似文献
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Xiangdong Yang 《复变函数与椭圆型方程》2016,61(3):351-358
Our purpose is to define composition operators acting upon Hardy spaces of Riemann surfaces. In terms of counting functions related to analytic self-map on Riemann surfaces, the boundedness and compactness are characterized. 相似文献
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Iryna Schlackow 《Topology and its Applications》2008,155(11):1227-1236
We study properties of Koszmider spaces and introduce a related notion of weakly Koszmider spaces. We show that if the space K is weakly Koszmider and C(K) is isomorphic to C(L) then L is also weakly Koszmider, but the analogous result does not hold for Koszmider spaces. We also show that a connected Koszmider space is strongly rigid. 相似文献
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In this paper,we study certain Hausdorf operators in the high-dimensional product spaces.We obtain their power weighted boundedness from Lpto Lqand characterize the necessary and sufcient conditions for their boundedness on the power weighted Lpspaces.Moreover,in the case p=q,we obtain the sharp bound constants. 相似文献
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Marian Nowak 《Proceedings of the American Mathematical Society》2007,135(9):2803-2809
Let be an ideal of over a -finite measure space , and let stand for the order dual of . For a real Banach space let be a subspace of the space of -equivalence classes of strongly -measurable functions and consisting of all those for which the scalar function belongs to . For a real Banach space a linear operator is said to be order-weakly compact whenever for each the set is relatively weakly compact in . In this paper we examine order-weakly compact operators . We give a characterization of an order-weakly compact operator in terms of the continuity of the conjugate operator of with respect to some weak topologies. It is shown that if is an order continuous Banach function space, is a Banach space containing no isomorphic copy of and is a weakly sequentially complete Banach space, then every continuous linear operator is order-weakly compact. Moreover, it is proved that if is a Banach function space, then for every Banach space any continuous linear operator is order-weakly compact iff the norm is order continuous and is reflexive. In particular, for every Banach space any continuous linear operator is order-weakly compact iff is reflexive.