In this article, we consider the spaceBp(D) (resp. ß) of functionswherehandkare holomorphic in a domainDinof classC3andfis inLp(D) (resp. the derivatives offof order 2 are majorized by the reciprocal of the square of distance to the boundary). We ask when the dual of B1can be identified with the space ß. In the case of holomorphic functions, B. Coupet has proved that the dual of the space of holomorphic functions, integrable over a strictly pseudoconvex domainDinof classC3can be identified with the Bloch space ß of holomorphic functions inDsuch thatfor everyzinD. First, following Bell's methods [1] we define the duality betweenB1and ß we prove that there exists a differential operatorLof order 2 continuous from ß toL∞ such that, ifPis the Bergman projection ofL2intoB2PLis equal to identity. This allows us to extend toB1×Bthe bilinear form on. Secondly, we prove that ß and the dual ofB1are isomorphic if and only if (1):B2is dense inB1and (2):PmapsL∞ intoB. In this case there exists a continuous projection ofL1intoB1. Following Carmona we prove that (1) is true for every open setDofsuch thathas a finite number of connected components, and that (2) can be expressed by estimations on the Bergman kernel forB2:We conclude that in the case of the unit disc, ß and the dual ofB1are isomorphic.