We introduce a natural generalization of a well-studied integration operator acting on the family of Hardy spaces in the unit disc. We study the boundedness and compactness properties of the operator and finally we use these results to give simple proofs of a result of Rättyä and another result by Cohn and Verbitsky.
Chalmoukis, N. (2020). Generalized integration operators on Hardy spaces. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 148(8), 3325-3337 [10.1090/proc/15016].
Generalized integration operators on Hardy spaces
Nikolaos Chalmoukis
2020
Abstract
We introduce a natural generalization of a well-studied integration operator acting on the family of Hardy spaces in the unit disc. We study the boundedness and compactness properties of the operator and finally we use these results to give simple proofs of a result of Rättyä and another result by Cohn and Verbitsky.
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