Multipliers on Weighted Besov Spaces of Analytic Functions

We characterize the space of multipliers between certain weighted Besov spaces of analytic functions. This extend and give a new proof of a result of Wojtaszczyk about multipliers between Bergman spaces. Introduction. P. Wojtaszczyk [W], using certain factorization theorems due to Maurey and Grothendieck, proved the following results: Let α > 0, 0 < p ≤ 2 ≤ q < ∞ and 1r = 1 p − 1q . (0.1) (Bq, Bp) = {λn : sup 2n≤k<2n+1 (k|λk|) ∈ l} (0.2) (Xα, Bp) = {λn : sup 2n≤k<2n+1 (k|λk|) ∈ l} where Bp and Xα stand for the spaces Bp = {f : D → C analytic : ( ∫ D |f(z)|dσ(z) )1/p < ∞} and Xα = {f : D → C analytic : |f(z)| = O( 1 (1 − |z|)α )}. The main objective of this paper is to extend such results to a much more general situation of general weighted Bergman and Besov spaces. We shall present a proof based simply on Kintchine’s inequality for the analogue to (0.1) and then we shall use the previous case combined with some duality arguments to get the analogue to (0.2). 1991 Mathematics Subject Classification. 42A45.