Action of convolution and Toeplitz operators in spaces of BMOA type. (Q1889471)

Let \(U\) be the unit disk, \(F_s^{\infty, q}(U)\) and BMOA\(_{\alpha, n, q, \beta}(U)\) two kinds of BMOA type spaces for \(s\in\mathbb{R}\), \(q\in (0, \infty)\), \(\alpha, \beta\geq0\), \(n\in\mathbb{N}\). The author first characterizes the coefficient multipliers from \(H^1(U)\) to \(F_s^{\infty, q}(U)\) and from \(A_\alpha^1(U)\) to \(F_s^{\infty, q}(U)\). Then a set of multipliers from \(A_\alpha^p(U)\) to \(F_s^{\infty, \nu}(U)\) is given. Finally, a theorem concerning division by an inner multiplier in spaces BMOA\(_{\alpha, n, q, \beta}(U)\) is proven. Suppose that the chain of inequalities \(\beta+1<q<\beta+2\), \(n\in\mathbb{N}\), \(\beta>0\), \(\alpha>0,\) holds. Then in the classes BMOA\(_{\alpha, n, q, \beta}(U)\), division by an inner function is possible.