• Strictly singular non-compact diagonal operators on HI spaces, Vol 36, No.3

Author: Stevo Stevic, Mathematical Institute of the Serbian Academy of Science, Knez Mihailova 36/III, 11000 Beograd, Serbia (sstevic@ptt.rs)
Strictly singular non-compact diagonal operators on HI spaces, pp. 843-858.
ABSTRACT. This paper studies the boundedness and compactness of extended Cesaro operators between mixed-norm spaces and Bloch-type spaces (or little Bloch-type spaces) of holomorphic functions on the unit ball. For the special (but still very general) case of the weighted Bergman space the paper calculates the norm of the operator for the case p>0 and finds some upper and lower bounds for the essential norm of the operator when p>1. When the reciprocal function of the weight appearing in the definition of the Bloch-type space is Lebesque integrable we completely characterized the boundedness and compactness of the operator from the Bloch-type spaces to the mixed-norm space.

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Strictly singular non-compact diagonal operators on HI spaces, Vol 36, No.3

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