New criteria for boundedness and compactness of weighted composition operators mapping into the Bloch space

作者：Colonna Flavia^*

来源：Central European Journal of Mathematics, 2013, 11(1): 55-73.

DOI：10.2478/s11533-012-0097-4

• Weighted composition operators
• Bloch space
• Hardy space
• Weighted Bergman space
• Dirichlet space

Let psi and phi be analytic functions on the open unit disk with phi() aS dagger . We give new characterizations of the bounded and compact weighted composition operators W (psi,I center dot) from the Hardy spaces H (p) , 1 a parts per thousand currency sign p a parts per thousand currency sign a, the Bloch space B, the weighted Bergman spaces A (alpha) (p) , alpha %26gt; - 1,1 a parts per thousand currency sign p %26lt; a, and the Dirichlet space to the Bloch space in terms of boundedness (respectively, convergence to 0) of the Bloch norms of W (psi,I center dot) f for suitable collections of functions f in the respective spaces. We also obtain characterizations of boundedness for H (1) as well as of compactness for H (p) , 1 a parts per thousand currency sign p %26lt; a, and purely in terms of the symbols psi and phi.

• 出版日期2013-1