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1.
It is proved that the Bergman type operatorT, is a bounded projection from the pluriharmonic Bergman spaceL
p
(B)∩h(B) onto Bergman spaceL
p
(B) ∩
H(B) for 0p 1 ands (p1-1)(n+1). As an application it is shown that the Gleason’s problem can be solved in Bergman space LP(B)∩H(B) for 0p 1.
Project supported by the National Natural Science Foundation of China (Grant No. 19871081) and the Doctoral Program Foundation
of the State Education Commission of China. 相似文献
2.
Jacob Burbea 《Rendiconti del Circolo Matematico di Palermo》1978,27(2):259-269
LetD be a bounded plane domain (with some smoothness requirements on its boundary). LetB p(D), 1≤p<∞, be the Bergmanp-space ofD. In a previous paper we showed that the “natural projection”P, involving the Bergman kernel forD, is a bounded projection fromL p(D) ontoB p(D), 1<p<∞. With this we have the decompositionL p(D)=B p(D)⊕B q ⊥ (D,p –1+q –=1, 1<p< ∞. Here, we show that the annihilatorB q ⊥ (D) is the space of allL p-complex derivatives of functions belonging to Sobolev space and which vanish on the boundary ofD. This extends a result of Schiffer for the casep=2. We also study certain operators onL p(D). Especially, we show that , whereI is the identity operator and ? is an operator involving the adjoint of the Bergman kernel. Other relationships relevant toB q ⊥ (D) are studied. 相似文献
3.
Manfred Stoll 《Monatshefte für Mathematik》2005,141(5):131-139
Let B denote the unit ball in [(?)\tilde] \widetilde{\nabla\hskip-4pt}\hskip4pt
denote the volume measure and gradient with respect to the Bergman metric on B. In the paper we consider the weighted Dirichlet spaces
Dg{{\cal D}_{\gamma}}
,
$\gamma > (n-1)$\gamma > (n-1)
, and weighted Bergman spaces
Apa{A^p_{\alpha}}
,
0 < p < ¥0 < p < \infty
,
$\alpha > n$\alpha > n
, of holomorphic functions f on B for which
Dg( f)D_{\gamma}(\,f)
and
|| f||Apa\Vert\, f\Vert_{A^p_{\alpha}}
respectively are finite, where
Dg( f)=òB (1-|z|2)g|[(?)\tilde] f(z)|2dt(z),D_{\gamma}(\,f)=\int_B (1-\vert z\vert^2)^{\gamma}\vert\widetilde{\nabla\hskip-4pt}\hskip4pt f(z)\vert^2d\tau(z),
and
|| f||pApa=òB(1-|z|2)a| f(z)|pdt(z).\Vert\, f\Vert^p_{A^p_{\alpha}}=\int_B(1-\vert z\vert^2)^{\alpha}\vert\, f(z)\vert^pd\tau(z).
The main result of the paper is the following theorem.Theorem 1. Let f be holomorphic on B and
$\alpha > n$\alpha > n
. 相似文献
4.
Austin Anderson 《Integral Equations and Operator Theory》2011,69(1):87-99
Our main result is a characterization of g for which the operator Sg(f)(z) = ò0z f¢(w)g(w) dw{S_g(f)(z) = \int_0^z f'(w)g(w)\, dw} is bounded below on the Bloch space. We point out analogous results for the Hardy space H
2 and the Bergman spaces A
p
for 1 ≤ p < ∞. We also show the companion operator Tg(f)(z) = ò0z f(w)g¢(w) dw{T_g(f)(z) = \int_0^z f(w)g'(w) \, dw} is never bounded below on H
2, Bloch, nor BMOA, but may be bounded below on A
p
. 相似文献
5.
Let X, Y be complex Banach spaces. Let G be a bounded balanced domain in X and B
Y
be the unit ball in Y. Assume that B
Y
is homogeneous. Let f: G → B
Y
be a holomorphic mapping. In this paper, we show that, if P = f(0), then we have Σ
k=0∞ ‖ D
φP
(P)[D
k
f(0)(z
k
)]‖/(k!‖D
φP
(P)‖) < 1 for z ∈ (1/3)G, where φP ∈ AutB
Y
) such that φP (P) = 0. Moreover, we show that the constant 1/3 is best possible, if B
Y
is the unit ball of a J*-algebra. The above result was proved by Liu and Wang in the case that G = B
Y
is one of the four classical domains in the sense of Hua. This result generalises a classical result of Bohr. 相似文献
6.
Djordjije Vujadinović 《Integral Equations and Operator Theory》2013,76(2):213-224
In this paper we obtain an estimate of the norm of the Bergman projection from L p (D, dλ) onto the Besov space B p , 1 < p < + ∞. The result is asymptotically sharp when p → + ∞. Further for the case P : L 1(D, dλ) → B 1, we consider some weak type inequalities with the corresponding spaces. 相似文献
7.
Xiao Jie 《数学学报(英文版)》1994,10(2):192-201
LetD={z∈Σ:|z|<1} and ϕ be a normal function on [0,1). Forp∈(0,1) such a function ϕ is used to define a Bergman spaceA
p
(ϕ) onD with weight ϕ
p
(|·|)/(1-|·|2). In this paper, the dual space ofA
p
(ϕ) is given, four characteristics of Carleson measure onA
p
(ϕ) are obtained. Moreover, as an application, three sequence interpolation theorems inA
p
(ϕ) are derived.
Supported by the Doctoral Program Foundation of Institute of Higher Education, P.R. China. 相似文献
8.
Zbigniew Błocki 《Inventiones Mathematicae》2013,193(1):149-158
We prove a conjecture of N. Suita which says that for any bounded domain D in ? one has $c_{D}^{2}\leq\pi K_{D}$ , where c D (z) is the logarithmic capacity of ??D with respect to z∈D and K D the Bergman kernel on the diagonal. We also obtain optimal constant in the Ohsawa-Takegoshi extension theorem. 相似文献
9.
Sharp estimates of the point-evaluation functional in weighted Bergman spaces L
p
a
(Ω, dν
α) and for the point-evaluation derivalive functional in Besov spaces B
p
(Ω) are obtained for bounded symmetric domains Ω in ℂ
n
.
Received October 25, 1999, Accepted December 6, 2000 相似文献
10.
Zhigang Peng 《Journal of Mathematical Analysis and Applications》2008,340(1):209-218
Let B denote the set of functions ?(z) that are analytic in the unit disk D and satisfy |?(z)|?1(|z|<1). Let P denote the set of functions p(z) that are analytic in D and satisfy p(0)=1 and Rep(z)>0(|z|<1). Let T denote the set of functions f(z) that are analytic in D, normalized by f(0)=0 and f′(0)=1 and satisfy that f(z) is real if and only if z is real (|z|<1). In this article we investigate the support points of the subclasses of B, P and T of functions with fixed coefficients. 相似文献