On a new integral-type operator from the weighted Bergman space to the Bloch-type space on the unit ball.

By S. Stević. 2008

76 citations recorded by the source corpus.

We introduce an integral-type operator, denoted by 𝑃𝑔𝜑, on the space of holomorphic functions on the unit ball 𝔹⊂ℂ𝑛, which is an extension of the product of composition and integral operators on the unit disk. The operator norm of 𝑃𝑔𝜑 from the weighted Bergman space 𝐴𝑝𝛼(𝔹) to the Bloch-type space ℬ𝜇(𝔹) or the little Bloch-type space ℬ𝜇,0(𝔹) is calculated. The compactness of the operator is characterized in terms of inducing functions 𝑔 and 𝜑. Upper and lower bounds for the essential norm of the operator 𝑃𝑔𝜑∶𝐴𝑝𝛼(𝔹)→ℬ𝜇(𝔹), when 𝑝>1, are also given.

Subfields: Algebra and Number Theory, Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/6b2b9c39fe308ac1cfec38a2443d3f4fed78155e

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In Algebra and Number Theory

In Applied Mathematics

Citations in the corpus

Products of composition and differentiation operators on the weighted Bergman space (2009, background): “Products of integral, differentiation and composition operators on spaces of analytic functions are studied in [4, 5, 11, 12, 13, 14, 16, 19, 29, 31, 34, 35].”