Convergence of the Cesàro mean for rational orthonormal bases

This paper deals with the convergence of the Cesaro mean for the rational orthonormal bases. Provided the set of zeroes of rational orthonormal bases is formed by a periodic repetition of the same finite sequence, the explicit expression of so-called block-Fejer kernel is available, and some properties of the block-Fejer kernel are discussed. Based on the convergence of the block-Cesaro mean, the convergence of Cesaro mean is also provided.     

Extended Cesáro operators from generally weighted Bloch spaces to Zygmund space

Let g be a holomorphic function of the unit ball B in the n-dimensional complex space, and denote by Tg the extended Cesáro operator with symbol g. Starting with a brief introduction to well-known results about Cesáro operator, we investigate the boundedness and compactness of Tg from generally weighted Bloch spaces (0<α<∞) to Zygmund space Z in the unit ball, and also present some necessary and sufficient conditions.     

Cesàro means of Jacobi expansions on the parabolic biangle

We study Cesàro (C,δ) means for two-variable Jacobi polynomials on the parabolic biangle . Using the product formula derived by Koornwinder and Schwartz for this polynomial system, the Cesàro operator can be interpreted as a convolution operator. We then show that the Cesàro (C,δ) means of the orthogonal expansion on the biangle are uniformly bounded if δ>α+β+1, α≥β≥0. Furthermore, for the means define positive linear operators.     

Growth order and stability of semigroups and cosine operator functions

Equivalent conditions for a trajectory of a C₀-semigroup T(⋅) (resp. cosine function C(⋅)) of operators to have the growth order O(tα) or o(tα) are expressed in terms of Cesàro and Abel means of the norm of the trajectory. We then deduce characterizations of growth order and stability for T(⋅) and C(⋅). It is also shown that under some Tauberian condition the uniform boundedness (resp. strong convergence) of T(⋅) is equivalent to the uniform boundedness (resp. strong convergence) of its Abel means.     

单位球上不同 Bergman空间之间的广义 Ces\`{a}ro 算子

In this paper,we obtain the characterizations on μ for（p,q）-φCarleson measure,and discuss the boundedness（and compactness） of the extended Cesaro operators T g between different weighted Bergman spaces as some application.