共查询到20条相似文献,搜索用时 46 毫秒
1.
M.C. Câmara 《Journal of Functional Analysis》2010,259(5):1273-1299
A meromorphic analogue to the corona problem is formulated and studied and its solutions are characterized as being left-invertible in a space of meromorphic functions. The Fredholmness of Toeplitz operators with symbol G∈(L∞(R))2×2 is shown to be equivalent to that of a Toeplitz operator with scalar symbol , provided that the Riemann-Hilbert problem admits a solution such that the meromorphic corona problems with data are solvable. The Fredholm properties are characterized in terms of and the corresponding meromorphic left-inverses. Partial index estimates for the symbols and Fredholmness criteria are established for several classes of Toeplitz operators. 相似文献
2.
Jie Miao 《Journal of Mathematical Analysis and Applications》2008,346(1):305-313
Let p>1 and let q denote the number such that (1/p)+(1/q)=1. We give a necessary condition for the product of Toeplitz operators to be bounded on the weighted Bergman space of the unit ball (α>−1), where and , as well as a sufficient condition for to be bounded on . We use techniques different from those in [K. Stroethoff, D. Zheng, Bounded Toeplitz products on Bergman spaces of the unit ball, J. Math. Anal. Appl. 325 (2007) 114-129], in which the case p=2 was proved. 相似文献
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Xiangrong Zhu 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(9):2890-2896
Let N be a compact Riemannian manifold. A self-similar solution for the heat flow is a harmonic map from to N (n≥3), which was also called a quasi-harmonic sphere (cf. Lin and Wang (1999) [1]). (Here is the Euclidean metric in .) It arises from the blow-up analysis of the heat flow at a singular point. When and without the energy constraint, we call this a quasi-harmonic function. In this paper, we prove that there is neither a nonconstant positive quasi-harmonic function nor a nonconstant quasi-harmonic function. However, for all 1≤p≤n/(n−2), there exists a nonconstant quasi-harmonic function in . 相似文献
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Hyungwoon Koo 《Journal of Functional Analysis》2008,254(11):2911-2925
We study composition operators CΦ on the Hardy spaces Hp and weighted Bergman spaces of the polydisc Dn in Cn. When Φ is of class C2 on , we show that CΦ is bounded on Hp or if and only if the Jacobian of Φ does not vanish on those points ζ on the distinguished boundary Tn such that Φ(ζ)∈Tn. Moreover, we show that if ε>0 and if , then CΦ is bounded on . 相似文献
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In this paper, the authors prove that Besov-Morrey spaces are proper subspaces of Besov-type spaces and that Triebel-Lizorkin-Morrey spaces are special cases of Triebel-Lizorkin-type spaces . The authors also establish an equivalent characterization of when τ∈[0,1/p). These Besov-type spaces and Triebel-Lizorkin-type spaces were recently introduced to connect Besov spaces and Triebel-Lizorkin spaces with Q spaces. Moreover, for the spaces and , the authors investigate their trace properties and the boundedness of the pseudo-differential operators with homogeneous symbols in these spaces, which generalize the corresponding classical results of Jawerth and Grafakos-Torres by taking τ=0. 相似文献
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Zhi Jie Jiang 《Applied mathematics and computation》2010,217(7):3522-3530
We characterize the compactness of differences of weighted composition operators from the weighted Bergman space , 0 < p < ∞, α > −1, to the weighted-type space of analytic functions on the open unit disk D in terms of inducing symbols and . For the case 1 < p < ∞ we find an asymptotically equivalent expression to the essential norm of these operators. 相似文献
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C.L. Prather 《Journal of Mathematical Analysis and Applications》2009,349(1):55-67
Let L=(1−x2)D2−((β−α)−(α+β+2)x)D with , and . Let f∈C∞[−1,1], , with normalized Jacobi polynomials and the Cn decrease sufficiently fast. Set Lk=L(Lk−1), k?2. Let ρ>1. If the number of sign changes of (Lkf)(x) in (−1,1) is O(k1/(ρ+1)), then f extends to be an entire function of logarithmic order . For Legendre expansions, the result holds with replaced with . 相似文献
10.
Jinlu Li 《Journal of Mathematical Analysis and Applications》2005,306(1):55-71
In this paper, we extend the definition of the generalized projection operator , where B is a reflexive Banach space with dual space B∗ and K is a nonempty, closed and convex subset of B and we study its properties and applications to solving variational inequality. 相似文献
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Let and be standard operator algebras on infinite dimensional complex Banach spaces X and Y, respectively, and let Φ be a unital additive surjection from onto . We introduce thirteen parts of the spectrum for elements in and , and prove that if Φ preserves any one of these parts of the spectrum, then it is either an isomorphism or an anti-isomorphism. 相似文献
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Gülen Ba?canbaz-Tunca 《Journal of Mathematical Analysis and Applications》2003,286(1):207-219
In this paper we investigate the spectrum and the spectral singularities of an operator L generalized in by the differential expression
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Liangping Jiang 《Journal of Mathematical Analysis and Applications》2007,326(2):1379-1382
The classical criterion of asymptotic stability of the zero solution of equations x′=f(t,x) is that there exists a function V(t,x), a(‖x‖)?V(t,x)?b(‖x‖) for some a,b∈K, such that for some c∈K. In this paper we prove that if f(t,x) is bounded, is uniformly continuous and bounded, then the condition that can be weakened and replaced by and contains no complete trajectory of , t∈[−T,T], where , uniformly for (t,x)∈[−T,T]×BH. 相似文献
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Matthew Neal 《Journal of Functional Analysis》2006,237(2):589-616
We construct some separable infinite-dimensional homogeneous Hilbertian operator spaces and , which generalize the row and column spaces R and C (the case m=0). We show that a separable infinite-dimensional Hilbertian JC∗-triple is completely isometric to one of , , , or the space Φ spanned by creation operators on the full anti-symmetric Fock space. In fact, we show that (respectively ) is completely isometric to the space of creation (respectively annihilation) operators on the m (respectively m+1) anti-symmetric tensors of the Hilbert space. Together with the finite-dimensional case studied in [M. Neal, B. Russo, Representation of contractively complemented Hilbertian operator spaces on the Fock space, Proc. Amer. Math. Soc. 134 (2006) 475-485], this gives a full operator space classification of all rank-one JC∗-triples in terms of creation and annihilation operator spaces.We use the above structural result for Hilbertian JC∗-triples to show that all contractive projections on a C∗-algebra A with infinite-dimensional Hilbertian range are “expansions” (which we define precisely) of normal contractive projections from A** onto a Hilbertian space which is completely isometric to R, C, R∩C, or Φ. This generalizes the well-known result, first proved for B(H) by Robertson in [A.G. Robertson, Injective matricial Hilbert spaces, Math. Proc. Cambridge Philos. Soc. 110 (1991) 183-190], that all Hilbertian operator spaces that are completely contractively complemented in a C∗-algebra are completely isometric to R or C. We use the above representation on the Fock space to compute various completely bounded Banach-Mazur distances between these spaces, or Φ. 相似文献
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In this paper, it is shown that the Berezin-Toeplitz operator Tg is compact or in the Schatten class Sp of the Segal-Bargmann space for 1?p<∞ whenever (vanishes at infinity) or , respectively, for some s with , where is the heat transform of g on Cn. Moreover, we show that compactness of Tg implies that is in C0(Cn) for all and use this to show that, for g∈BMO1(Cn), we have is in C0(Cn) for some s>0 only if is in C0(Cn) for alls>0. This “backwards heat flow” result seems to be unknown for g∈BMO1 and even g∈L∞. Finally, we show that our compactness and vanishing “backwards heat flow” results hold in the context of the weighted Bergman space , where the “heat flow” is replaced by the Berezin transform Bα(g) on for α>−1. 相似文献
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It was well known that Calderón-Zygmund operators T are bounded on Hp for provided T∗(1)=0. A new Hardy space , where b is a para-accretive function, was introduced in [Y. Han, M. Lee, C. Lin, Hardy spaces and the Tb-theorem, J. Geom. Anal. 14 (2004) 291-318] and the authors proved that Calderón-Zygmund operators T are bounded from the classical Hardy space Hp to the new Hardy space if T∗(b)=0. In this note, we give a simple and direct proof of the boundedness of Calderón-Zygmund operators via the vector-valued singular integral operator theory. 相似文献
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Tsehaye K. Araaya 《Journal of Mathematical Analysis and Applications》2005,305(2):411-423
The Symmetric Meixner-Pollaczek polynomials for λ>0 are well-studied polynomials. These are polynomials orthogonal on the real line with respect to a continuous, positive real measure. For λ?0, are also polynomials, however they are not orthogonal on the real line with respect to any real measure. This paper defines a non-standard inner product with respect to which the polynomials for λ?0, become orthogonal polynomials. It examines the major properties of the polynomials, for λ>0 which are also shared by the polynomials, for λ?0. 相似文献
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Hiroaki Terao 《Advances in Mathematics》2007,214(1):366-378
Let A be a nonempty real central arrangement of hyperplanes and Ch be the set of chambers of A. Each hyperplane H defines a half-space H+ and the other half-space H−. Let B={+,−}. For H∈A, define a map by (if C⊆H+) and (if C⊆H−). Define . Let Chm=Ch×Ch×?×Ch (m times). Then the maps induce the maps . We will study the admissible maps which are compatible with every . Suppose |A|?3 and m?2. Then we will show that A is indecomposable if and only if every admissible map is a projection to a component. When A is a braid arrangement, which is indecomposable, this result is equivalent to Arrow's impossibility theorem in economics. We also determine the set of admissible maps explicitly for every nonempty real central arrangement. 相似文献