Divergence of Cesàro means of spherical h-harmonic expansions

A divergence result for Cesàro means of spherical h-harmonics expansions with a product weight is proved in this short note.     

On Cesàro means, Kaplan classes and a conjecture of S.P. Robinson

We establish special cases of a conjecture of S.P. Robinson [S.P. Robinson, Approximate identities for certain dual classes, DPhil thesis, University of York, UK, 1996] concerning Cesàro means of certain classes of analytic functions in the unit disk. This has applications, for instance, to the so-called Kaplan classes and subordination under ‘linearly accessible’ functions.     

A short proof of some recent results related to Cesàro function spaces

We give a short proof of the recent results that, for every 1≤p<∞$1\le p<\infty$, the Cesàro function space Ce_sp(I)$Ce{s}_p\left(I\right)$ is not a dual space, has the weak Banach–Saks property and does not have the Radon–Nikodym property.     

Dirichlet空间上Toeplitz算子的一些性质

该文研究了Dirichlet空间D^p~(1< p<∞)上Toeplitz算子的紧性与Fredholm性质, 计算了D^p上Toeplitz算子的Fredholm指标. 还考查了D^p上Hankel算子紧性.     

Hilbert空间上算子W-加权Drazin逆的刻画及表示

该文研究了Hilbert空间上线性算子的W-加权Drazin逆,利用算子的分块矩阵表示,给出了W-加权Drazin逆的刻画及表示,所获结果推广了魏益民等的相关结果.     

The Hausdorff operator is bounded on the real Hardy space

We prove that the Hausdorff operator generated by a function is bounded on the real Hardy space . The proof is based on the closed graph theorem and on the fact that if a function in is such that its Fourier transform equals for (or for ), then .

     

Strong Cesàro summability of double Fourier integrals

We prove the following theorem. Assume f ∈ L ^∞(R ²) with bounded support. If f is continuous at some point (x ₁,x ₂) ∈ R ², then the double Fourier integral of f is strongly q-Cesàro summable at (x ₁,x ₂) to the function value f(x ₁,x ₂) for every 0 < q < ∞. Furthermore, if f is continuous on some open subset of R ², then the strong q-Cesàro summability of the double Fourier integral of f is locally uniform on . Research partially supported by the Australian Research Council and the Hungarian National Foundation for Scientific Research under Grant T 046 192.