Sharp Norm Estimates for Weighted Bergman Projections in the Mixed Norm Spaces

In this paper, we show that the norm of the Bergman projection on L^p,q-spaces in the upper half-plane is comparable to csc(π/q). Then we extend this result to a more general class of domains, known as the homogeneous Siegel domains of type II.     

Sharp Estimates in Bergman and Besov Spaces on Bounded Symmetric Domains

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     

Essential Norm Estimates for Little Hankel Operators on Weighted Bergman Spaces of the Unit Ball

We give estimates for the essential norm of a bounded little Hankel operator with $L^2$ symbol on weighted Bergman spaces of the unit ball in terms of a certain integral transform of the symbol. As an application of these estimates, we also give a necessary and sufficient condition for the little Hankel operators to be compact.     

Norm Approximation by Polynomials in Some Weighted Bergman Spaces

The polynomials are shown to be dense in weighted Bergman spaces in the unit disk whose weights are superbiharmonic and vanish in an average sense at the boundary. This leads to an alternative proof of the Aleman-Richter-Sundberg Beurling-type theorem for zero-based invariant subspaces in the classical Bergman space. Additional consequences are deduced.     

Univalent Interpolation in Besov Spaces and Superposition into Bergman Spaces

We establish the best possible condition for point singularities to be removable for nonlinear elliptic equations in divergent form with lower order terms from the non-linear Kato classes.      

单位球上Bergman空间到Besov空间的广义Cesaro算子(英文)

本文利用Carleson测度刻画了Bergman空间到Besov空间的广义Cesaro算子T_g的有界性和紧性,同时得到了(p,q)-φCarleson测度的一些性质.     

Some Applications of Besov Spaces on Fractals

Let F be a compact d-set in R^n with 0 〈 d ≤ n, which includes various kinds of fractals. The author establishes an embedding theorem for the Besov spaces Bpq^s（F） of Triebel and the Sobolev spaces W^1,P（F,d,μ） of Hajtasz when s 〉 1, 1 〈 p 〈∞ and 0 〈 q ≤ ∞. The author also gives some applications of the estimates of the entropy numbers in the estimates of the eigenvalues of some fractal pseudodifferential operators in the spaces Bpq^0（F） and Fpq^0（F）.     

On Maximum Norm Estimates for Ritz-Volterra Projection with Applications to Some Time Dependent Problems

1.IntroductionWeareconcernedwiththefiniteelementmethodforparabolicintegro-differentialequationwhereV(t)isingeneralaniniegro-differentialoperatordefinedonaHilbertspaceXandthatuandfareX-valuedfunctionsdefinedonJ~(0,T)withapositivetimeT.AtypicalexampleoftheHilbertspaceXintheapplicationwillbetheSobolevspaceHIconsistingoffunctionsdefinedonanopenboundeddomainfiwithvanishedboundaryvalueandfirstorderderivativessummableinL',whiletheoperatorV(t)istheonedefinedbyforanyu(t)EHi(fl),whereA(t)isalinear…     

Norm Estimates for Weighted Composition Operators on Spaces of Holomorphic Functions

This paper shows that the boundedness of a weighted composition operator on the Hardy–Hilbert space on the disc or half-plane implies its boundedness on a class of related spaces, including weighted Bergman spaces. The methods used involve the study of lower-triangular and causal operators.     

Bergman空间上Hankel算子的本性范数的刻划

在文中,对于Ｃ＾ｍ中有界强拟凸域Ω,得到了Ｂｅｒｇｍａｎ空间Ａ＾２（Ω）上的Ｈａｎｋｅｌ算子Ｈｆ（ｆ∈Ｌ＾２（Ω,ｄｖ）的本性范数∥Ｈｆ∥ｅｓｓ（在Ｌ＾２（Ω,ｄｖ上）的等价刻划。     

Norm of an Integral Operator Related to the Harmonic Bergman Projection

The norm of the operator

Hankel Operators on Fock Spaces and Related Bergman Kernel Estimates

Hankel operators with anti-holomorphic symbols are studied for a large class of weighted Fock spaces on ? ⁿ . The weights defining these Hilbert spaces are radial and subject to a mild smoothness condition. In addition, it is assumed that the weights decay at least as fast as the classical Gaussian weight. The main result of the paper says that a Hankel operator on such a Fock space is bounded if and only if the symbol belongs to a certain BMOA space, defined via the Berezin transform. The latter space coincides with a corresponding Bloch space which is defined by means of the Bergman metric. This characterization of boundedness relies on certain precise estimates for the Bergman kernel and the Bergman metric. Characterizations of compact Hankel operators and Schatten class Hankel operators are also given. In the latter case, results on Carleson measures and Toeplitz operators along with Hörmander’s L ² estimates for the $\bar{\partial}$ operator are key ingredients in the proof.     

On Some Properties of Superreflexive Besov Spaces

Doklady Mathematics - This paper contains results concerning superreflective Besov spaces $$B_{{p,q}}^{s}({{\mathbb{R}}^{n}})$$ . Namely, expressions for convexity moduli and smoothness moduli with...     

Bochner-Riesz算子在加权Morrey空间上的一些估计

要本文将得到Bochner-Riesz算子T_R~((n-1)/2)在加权Morrey空间L~(p,k)(w)上的一些强型和弱型估计,1≤P<∞且0相似文献   

Some New Extrapolation Estimates for the Scale of Spaces

Using new extrapolation estimates for the - and -functionals of couples of limit spaces of the -scale , we introduce a class of extrapolation functors. A characterization of this class via the real interpolation method permits one to obtain new equivalent expressions for the norms in symmetric spaces close to and , which depend only on the -norms of a function.     

加权Begman空间的加权复合算子的本性模

利用上极限,给出了单位球上加权Bergman空间的加权复合算子的本性模的表示．     

The Essential Norm of Hankel Operators on the Weighted Bergman Spaces with Exponential Type Weights

Let denote the closed subspace of consisting of analytic functions in the unit disc . For certain class of subharmonic functions and , it is shown that the essential norm of Hankel operator is comparable to the distance norm from H_f to compact Hankel operators.     

Greedy Bases for Besov Spaces

We prove that the Banach space (?_n=1^￥l_pⁿ)_lq(\bigoplus_{n=1}^{\infty}\ell_{p}^{n})_{\ell_{q}}, which is isomorphic to certain Besov spaces, has a greedy basis whenever 1≤p≤∞ and 1<q<∞. Furthermore, the Banach spaces (?_n=1^￥l_pⁿ)_l1(\bigoplus_{n=1}^{\infty}\ell _{p}^{n})_{\ell_{1}}, with 1<p≤∞, and (?_n=1^￥l_pⁿ)_c0(\bigoplus_{n=1}^{\infty}\ell_{p}^{n})_{c_{0}}, with 1≤p<∞, do not have a greedy basis. We prove as well that the space (?_n=1^￥l_pⁿ)_lq(\bigoplus_{n=1}^{\infty}\ell _{p}^{n})_{\ell_{q}} has a 1-greedy basis if and only if 1≤p=q≤∞.     

Interpolating Sequences for Besov Spaces

We characterise the interpolating sequences for the Besov spaces B_p and for their multiplier spaces. We also construct linear operators of interpolation.     

Some Estimates for the Fourier Transform on Rank 1 Symmetric Spaces

Two estimates useful in applications are proved for the Fourier transform in the space L~2(X), where X a symmetric space, as applied to some classes of functions characterized by a generalized modulus of continuity.