Girela, Daniel; Merchán, Noel Multipliers and integration operators between conformally invariant spaces. (English) Zbl 1455.30048 Rev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat., RACSAM 114, No. 4, Paper No. 181, 22 p. (2020). For various couples \((X,Y)\) of Möbius invariant function spaces \(X,Y\) on the disk, the authors give characterizations of those symbols \(g\in H(\mathbb D)\) for which the operators \(T_g\),\(I_g\) or \(M_g\) map \(X\) into \(Y\). Here \(T_g(f)(z)=\int_0^z g'(\xi)f(\xi)d\xi\), \(I_g(f)(z)=\int_0^z g(\xi)f'(\xi)d\xi\) and \(M_g(f)(z)= g(z)f(z)\) and a relation is given by \(T_g(f)+I_g(f)=M_g(f)-f(0)g(0)\). Spaces considered are weighted Bergman spaces \(A^p_\alpha\), Besov spaces, \(Q_s\)-spaces, Bloch spaces, BMOA and VMOA. Briefly studied is also the subject whether some of the multiplier spaces \(R=M(X,Y)\) have the \(f\)-property (meaning that if \(g\in R\) and \( g/I\in H^1\), then \(g/I\in R\) for any inner divisor \(I\) in \(H^1\)). Reviewer: Raymond Mortini (Metz) Cited in 3 Documents MSC: 30H25 Besov spaces and \(Q_p\)-spaces 47B38 Linear operators on function spaces (general) 30H30 Bloch spaces Keywords:Möbius invariant spaces; Bloch space; Besov spaces; \(Q_s\); multipliers; integration operators; Carleson measures; f-property PDFBibTeX XMLCite \textit{D. Girela} and \textit{N. Merchán}, Rev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat., RACSAM 114, No. 4, Paper No. 181, 22 p. (2020; Zbl 1455.30048) Full Text: DOI arXiv References: [1] Aleman, A.; Cima, JA, An integral operator on \(H^p\) and Hardy’s inequality, J. Anal. Math., 85, 157-176 (2001) · Zbl 1061.30025 [2] Aleman, A.; Duren, PL; Martín, MJ; Vukotić, D., Multiplicative isometries and isometric zero-divisors, Can. J. Math., 62, 5, 961-974 (2010) · Zbl 1210.30018 [3] Aleman, A.; Simbotin, A., Estimates in Möbius invariant spaces of analytic functions, Complex Var. 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