Journal
ANNALS OF FUNCTIONAL ANALYSIS
Volume 13, Issue 3, Pages -Publisher
SPRINGER BASEL AG
DOI: 10.1007/s43034-022-00193-6
Keywords
Projective limits; Embeddings; Bloch-type spaces; Composition operators; Mobius invariant function spaces
Categories
Funding
- TUBITAK project [118F405]
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In this paper, we prove that the projective limit of a certain class of Dirichlet-type spaces is isomorphic to the Bloch-type spaces B-alpha. We provide a complete characterization of bounded or compact embeddings of B-alpha into a family of Lebesgue spaces by the derivative operator. As an application, we prove precise necessary and sufficient criteria for boundedness/compactness of the generalized composition operators. The Dirichlet-type intermediate spaces constructed in this paper serve very useful.
In this paper, we prove that the projective limit of a certain class of Dirichlet-type spaces is isomorphic to the Bloch-type spaces B-alpha. We provide a complete characterization of bounded or compact embeddings of B-alpha into a family of Lebesgue spaces by the derivative operator. As an application, we prove precise necessary and sufficient criteria for boundedness/compactness of the generalized composition operators. The Dirichlet-type intermediate spaces constructed in this paper serve very useful.
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