On a New Integral-Type Operator from the Weighted Bergman Space to the Bloch-Type Space on the Unit Ball

Stevo Stević

Discrete Dynamics in Nature and Society, 2008, vol. 2008, 1-14

Abstract:

We introduce an integral-type operator, denoted by 𠑃 ð ‘” 𠜑 , on the space of holomorphic functions on the unit ball ð ”¹ ⊂ â„‚ ð ‘› , which is an extension of the product of composition and integral operators on the unit disk. The operator norm of 𠑃 ð ‘” 𠜑 from the weighted Bergman space ð ´ ð ‘ ð ›¼ ( ð ”¹ ) to the Bloch-type space ℬ 𠜇 ( ð ”¹ ) or the little Bloch-type space ℬ 𠜇 , 0 ( ð ”¹ ) is calculated. The compactness of the operator is characterized in terms of inducing functions ð ‘” and 𠜑 . Upper and lower bounds for the essential norm of the operator 𠑃 ð ‘” 𠜑 ∶ ð ´ ð ‘ ð ›¼ ( ð ”¹ ) → ℬ 𠜇 ( ð ”¹ ) , when ð ‘ > 1 , are also given.

Date: 2008
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnddns:154263

DOI: 10.1155/2008/154263

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