Abstract. In the paper we find, for certain values of the parameters, the spaces of multipliers H (p, q, α), H(s, t, β) and H(p, q, α), l s , where H(p, q, α) denotes the space of analytic functions on the unit disc such thatAs corollaries we recover some new results about multipliers on Bergman spaces and Hardy spaces. §0.Introduction.Given two sequence spaces X and Y , we denote by (X, Y ) the space of multipliers from X into Y , that is the space of sequences of complex numbers (λ n ) such that (λ n a n ) ∈ Y for (a n ) ∈ X.When dealing with spaces of analytic functions defined on the open unit disc D we associate to each analytic function f (z) = ∞ n=0 a n z n the corresponding sequence of Taylor coefficients (a n ). In this sense any space of analytic functions is regarded as a sequence space and it makes sense to study multipliers acting on different classes of spaces such as Hardy spaces, Bergman spaces and so on. The aim of this paper is to study spaces of multipliers acting on certain general classes of analytic functions, denoted by H (p, q, α), which consists of functions on the unit disc such thatThe definition of these classes goes back to the work of Hardy and Littlewood (see [HL1,HL2]) and they were intensively studied for different reasons and by several authors. The reader is referred to the papers [DRS,F1,F2,MP1,S1,Sh] for information and properties on the spaces.There are two different techniques used in the paper. On one hand the use of a general theorem on operators acting on H(p, q, α) for 0 < p ≤ 1 which allows us to find H (p, q, α), H(s, t, β) and H(p, q, α), l s for the cases 0 < p, q ≤ 1 and 1 ≤ s, t ≤ ∞ and also for 0 < p ≤ 1 ≤ q although only for particular cases of s and t. In particular we can get a proof of the recent theorem, due to M. Mateljevic and 1991 Mathematics Subject Classification. 42A45.

We study the rate of growth of entire functions that are frequently hypercyclic for the differentiation operator or the translation operator. Moreover, we prove the existence of frequently hypercyclic harmonic functions for the translation operator and we study the rate of growth of harmonic functions that are frequently hypercyclic for partial differentiation operators.

Abstract. The Bloch space has been studied on the open unit disk of C and some homogeneous domains of C n . We define Bloch functions on the open unit ball of a Hilbert space E and prove that the corresponding space B(BE) is invariant under composition with the automorphisms of the ball, leading to a norm that-modulo the constant functionsis automorphism invariant as well. All bounded analytic functions on BE are also Bloch functions.

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We prove here that the Hardy space of B-valued functions H1{B) defined by using the conjugate function and the one defined in terms of Bvalued atoms do not coincide for a general Banach space. The condition for them to coincide is the UMD property on B. We also characterize the dual space of both spaces, the first one by using B'-valued distributions and the second one in terms of a new space of vector-valued measures, denoted SSJfcfiB"), which coincides with the classical BMO(B*) of functions when B* has the RNP.