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Isometric composition operators for the Möbius invariant H p norm of BMOA
Author(s) -
Pouliasis Stamatis
Publication year - 2021
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms.12434
Subject(s) - mathematics , isometry (riemannian geometry) , holomorphic function , invariant (physics) , unit disk , pure mathematics , hardy space , logarithm , composition operator , norm (philosophy) , mathematical analysis , multiplication operator , mathematical physics , hilbert space , political science , law
We characterize the holomorphic self‐maps of the unit disk for which the corresponding composition operator is an isometry of BMOA equipped with the Möbius invariant H p norm, answering a question posed by Laitila, for p ∈ [ 1 , 2 ) . Also, we show that the image of the symbol of an isometric composition operator for BMOA, with respect to the Möbius invariant H p norm, p ∈ [ 1 , + ∞ ) , covers the whole unit disc except a set of zero logarithmic capacity.