Weighted composition operators from weighted Bergman spaces to weighted-type spaces on the unit ball

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.     

Compact differences of weighted composition operators from weighted Bergman spaces to weighted-type spaces

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.     

Commuting dual Toeplitz operators on weighted Bergman spaces of the unit ball

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.     

Difference of composition operators between standard weighted Bergman spaces

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.     

Integral-type operators acting between weighted-type spaces on the unit ball

Let B denote the unit ball in Cⁿ and H(B) the space of all holomorphic functions on B. We study the boundedness and compactness of the following integral-type operators

     

Essential norm of differences of weighted composition operators between weighted-type spaces on the unit ball

We find an asymptotically equivalent expression to the essential norm of differences of weighted composition operators between weighted-type spaces of holomorphic functions on the unit ball in C^N. As a consequence we characterize the compactness of these operators. The boundedness of these operators is also characterized.     

Weighted composition operators from the weighted Bergman space to the weighted Hardy space on the unit ball

We investigate the weighted composition operator from the weighted Bergman space into the weighted Hardy space on the unit ball. As a consequence of the investigation, we also give a characterization for the boundedness and compactness of the operator whose the target space is the Hardy space.     

On norms of composition operators acting on Bergman spaces

For arbitrary composition operators acting on a general Bergman space we improve the known lower bound for the norm and also generalize a related recent theorem of D.G. Pokorny and J.E. Shapiro. Next, we obtain a geometric formula for the norms of composition operators with linear fractional symbols, thus extending a result of C. Cowen and P. Hurst and revealing the meaning of their computation. Finally, we obtain a lower bound for essential norm of an arbitrary composition operator related to the well-known criterion of B. MacCluer and J.H. Shapiro. As a corollary, norms and essential norms are obtained for certain univalently induced noncompact composition operators in terms of the minimum of the angular derivative of the symbol.     

Essential norms of weighted composition operators from weighted Bergman space to mixed-norm space on the unit ball

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.     

Bounded Toeplitz products on the weighted Bergman spaces of the unit ball

Let p>1 and let q denote the number such that (1/p)+(1/q)=1. We give a necessary condition for the product of Toeplitz operators to be bounded on the weighted Bergman space of the unit ball (α>−1), where and , as well as a sufficient condition for to be bounded on . We use techniques different from those in [K. Stroethoff, D. Zheng, Bounded Toeplitz products on Bergman spaces of the unit ball, J. Math. Anal. Appl. 325 (2007) 114-129], in which the case p=2 was proved.     

Dynamics of weighted composition operators in the unit ball

In the present paper, we investigate the dynamic behavior of weighted composition operators acting on the space of holomorphic functions on the unit ball in ${\mathbb{C}}^N$.     

WEIGHTED COMPOSITION OPERATORS BETWEEN BERS-TYPE SPACES AND BERGMAN SPACES

This paper characterizes the boundedness and compactness of weighted composition operators between Bers-type space （or little Bers-type space） and Bergman space. Some estimates for the norm of weighted composition operators between those spaces are obtained.