In this article, we study the existence of solutions of the complex linear differential equation of the form f (n) + An−1(z)f (n−1) + ... + A1(z)f + A0(z)f = 0, where the coefficients A0, A1, ..., An are analytic functions in the unit disc. To carry out the existence of these solutions, we obtain some conditions for the coefficients which grantee the existence of the solutions in QK,ω(p, q) spaces.
Abstract. In this paper, we study Lipschitz continuous, the boundedness and compactness of the composition operator C φ acting between the general hyperbolic Bloch type-classes B * p,log,α and general hyperbolic Besov-type classes F * p,log (p, q, s). Moreover, these classes are shown to be complete metric spaces with respect to the corresponding metrics.
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