Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 41, 2016, 199-220

BOUNDARY MULTIPLIERS OF A FAMILY OF MÖBIUS INVARIANT FUNCTION SPACES

Guanlong Bao and Jordi Pau

Shantou University, Department of Mathematics
Shantou, Guangdong 515063, P.R. China; glbaoah 'at' 163.com

Universitat de Barcelona, Departament de Matemática Aplicada i Analisi
08007 Barcelona, Spain; jordi.pau 'at' ub.edu

Abstract. For 1 < p < ∞ and 0 < s < 1, we consider the function spaces Q_s^p(T) that appear naturally as the space of boundary values of a certain family of analytic Möbius invariant function spaces on the the unit disk. In this paper, we give a complete description of the pointwise multipliers going from Q_s^p1(T) to Q_r^p2(T) for all ranges of 1 < p₁,p₂ < ∞ and 0 < s,r < 1. The spectra of such multiplication operators is also obtained.

2010 Mathematics Subject Classification: Primary 30H25, 30J10, 46E15.

Key words: Pointwise multipliers, Carleson measures, Blaschke products, Q_s^p(T) spaces.

Reference to this article: G. Bao and J. Pau: Boundary multipliers of a family of Möbius invariant function spaces. Ann. Acad. Sci. Fenn. Math. 41 (2016), 199-220.

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doi:10.5186/aasfm.2016.4113