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Pointwise multipliers between spaces of analytic functions.
- Source :
-
QM - Quaestiones Mathematicae . Mar2024, Vol. 47 Issue 2, p249-262. 14p. - Publication Year :
- 2024
-
Abstract
- A Banach space X of analytic function in , the unit disc in , is said to be admissible if it contains the polynomials and convergence in X implies uniform convergence in compact subsets of. If X and Y are two admissible Banach spaces of analytic functions in and g is a holomorphic function in , g is said to be a multiplier from X to Y if g ·f ∈ Y for every f ∈ X. The space of all multipliers from X to Y is denoted M (X, Y), and M (X) will stand for M (X, X). The closed graph theorem shows that if g ∈ M (X, Y) then the multiplication operator Mg, defined by Mg (f) = g · f, is a bounded operator from X into Y. It is known that M (X) ⊂ H∞ and that if g ∈ M (X), then ∥g∥H∞ ≤ ||Mg||. Clearly, this implies that M (X, Y) ⊂ H∞ if Y ⊂ X. If Y ⊄ X, the inclusion M (X, Y) ⊂ H∞ may not be true. In this paper we start presenting a number of conditions on the spaces X and Y which imply that the inclusion M (X, Y) ⊂ H∞ holds. Next, we concentrate our attention on multipliers acting an BMOA and some related spaces, namely, the Qs-spaces (0<s<∞). [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 16073606
- Volume :
- 47
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- QM - Quaestiones Mathematicae
- Publication Type :
- Academic Journal
- Accession number :
- 176721421
- Full Text :
- https://doi.org/10.2989/16073606.2023.2223766