共查询到20条相似文献,搜索用时 15 毫秒
1.
江治杰 《纯粹数学与应用数学》2010,26(6):984-991
通过再生核函数刻画了Hardy空间,Bergman空间上自伴加权复合算子以及自伴等距加权复合算子,最后研究了单位球上的分式线性自同构,得到了一个充分条件。 相似文献
2.
Ali Abkar 《Czechoslovak Mathematical Journal》2007,57(3):877-883
We consider a nonnegative superbiharmonic function w satisfying some growth condition near the boundary of the unit disk in the complex plane. We shall find an integral representation
formula for w in terms of the biharmonic Green function and a multiple of the Poisson kernel. This generalizes a Riesz-type formula already
found by the author for superbihamonic functions w satisfying the condition 0 ⩽ w(z) ⩽ C(1-|z|) in the unit disk. As an application we shall see that the polynomials are dense in weighted Bergman spaces whose weights
are superbiharmonic and satisfy the stated growth condition near the boundary.
Research supported in part by IPM under the grant number 83310011. 相似文献
3.
4.
Miroslav Engliš 《Journal of Functional Analysis》2008,255(6):1419-1457
For a smoothly bounded strictly pseudoconvex domain, we describe the boundary singularity of weighted Bergman kernels with respect to weights behaving like a power (possibly fractional) of a defining function, and, more generally, of the reproducing kernels of Sobolev spaces of holomorphic functions of any real order. This generalizes the classical result of Fefferman for the unweighted Bergman kernel. Finally, we also exhibit a holomorphic continuation of the kernels with respect to the Sobolev parameter to the entire complex plane. Our main tool are the generalized Toeplitz operators of Boutet de Monvel and Guillemin. 相似文献
5.
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
6.
Anders Olofsson 《Mathematische Nachrichten》2009,282(10):1451-1460
We show that operator-valued Bergman inner functions have the so-called expansive multiplier property generalizing a well-known result of Hedenmalm in the scalar case. This analysis leads to norm bounds for input output maps for a related class of discrete time linear systems. The proof uses properties of the biharmonic Green function (© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
7.
Erno Saukko 《Journal of Mathematical Analysis and Applications》2011,381(2):789-798
We obtain estimates for the norm and essential norm of the difference of two composition operators between certain Bergman spaces. In particular, a necessary and sufficient condition for boundedness and compactness of the operator is established. Finally, we give a sufficient condition for boundedness and compactness of the difference operator between Hardy spaces. 相似文献
8.
This paper gives a note on weighted composition operators on the weighted Bergman space, which shows that for a fixed composition symbol, the weighted composition operators are bounded on the weighted Bergman space only with bounded weighted symbols if and only if the composition symbol is a finite Blaschke product. 相似文献
9.
Tatiana V. Savina 《Journal of Mathematical Analysis and Applications》2010,370(2):716-1163
The biharmonic equation arises in areas of continuum mechanics including linear elasticity theory and the Stokes flows, as well as in a radar imaging problem. We discuss the reflection formulas for the biharmonic functions u(x,y)∈R2 subject to different boundary conditions on a real-analytic curve in the plane. The obtained formulas, generalizing the celebrated Schwarz symmetry principle for harmonic functions, have different structures. In particular, in the special case of the boundary, Γ0:={y=0}, reflections are point-to-point when the given on Γ0 conditions are u=n∂u=0, u=Δu=0 or n∂u=n∂Δu=0, and point to a continuous set when u=n∂Δu=0 or n∂u=Δu=0 on Γ0. 相似文献
10.
In this paper, we characterize the boundedness and compactness of the weighted composition operators from the weighted Bergman space to the standard mixed-norm space or the mixed-norm space with normal weight on the unit ball and estimate the essential norms of the weighted composition operators. 相似文献
11.
Boo Rim Choe Hyungwoon Koo Young Joo Lee 《Transactions of the American Mathematical Society》2004,356(5):1727-1749
We obtain characterizations of (essentially) commuting Toeplitz operators with pluriharmonic symbols on the Bergman space of the polydisk. We show that commuting and essential commuting properties are the same for dimensions bigger than 2, while they are not for dimensions less than or equal to 2. Also, the corresponding results for semi-commutators are obtained.
12.
Forα1,let dvαdenote the weighted Lebesgue measure on the bidisk andμa complex measure satisfying some Carleson-type conditions.In this paper,we show a sufcient and necessary condition for the Toeplitz operatorTαˉμto be bounded or compact on weighted Bergman spaceL1a(dvα). 相似文献
13.
In this paper, we study composition operators on a Banach space of analytic functions, denoted byX, which includes the Bloch space. This space arises naturally as the dual space of analytic functions in the Bergman spaceL
α
1
(D) which admit an atomic decomposition. We characterize the functions which induce compact composition operators and those
which induce Fredholm operatorson this space. We also investigate when a composition operator has a closed range.
Supported by NNSFC No.19671036 相似文献
14.
María J. Martín 《Journal of Functional Analysis》2006,238(1):298-312
We observe that a formula for the adjoint of a composition operator, known only for special symbols in some spaces of analytic functions, actually holds for every admissible symbol and in any Hilbert space of analytic functions with reproducing kernels. Along with some new results, all known formulas for the adjoint obtained so far follow easily as a consequence, some in an improved form. 相似文献
15.
Composition operators between weighted Bergman spaces with a smaller exponent in the target space are studied. An integrability condition on a generalized Nevanlinna counting function of the inducing map is shown to characterize both compactness and boundedness of such an operator. Composition operators mapping into the Hardy spaces are included by making particular choices for the weights.
16.
In this paper, we study the commutativity of dual Toeplitz operators on weighted Bergman spaces of the unit ball. We obtain
the necessary and sufficient conditions for the commutativity, essential commutativity and essential semi-commutativity of
dual Toeplitz operator on the weighted Bergman spaces of the unit ball. 相似文献
17.
Weighted composition operators from weighted Bergman spaces to weighted-type spaces on the unit ball
Stevo Stevi? 《Applied mathematics and computation》2009,212(2):499-504
We calculate the operator norm of the weighted composition operator from a weighted Bergman space to a weighted-type space on the unit ball of Cn. We also characterize the compactness of the operator. 相似文献
18.
Qiaoling Wang 《Journal of Mathematical Analysis and Applications》2010,364(1):1-17
In this paper, we study the eigenvalues of the clamped plate problem:
19.
Michael Ulm 《Proceedings of the American Mathematical Society》1999,127(2):481-489
For an operator on a Banach lattice we examine the interval on the real line for which the resolvent is positive. This positivity interval is then explicitly calculated for the biharmonic operator with three different boundary conditions.
20.
给出了一些次线性算子从加权Herz空间到加权弱Herz空间的有界性证明。 相似文献