[EN] We study bilinear operators acting on a product of Hilbert spaces of integrable functions¿zero-valued for couples of functions whose convolution equals zero¿that we call convolution-continuous bilinear maps. We prove a factorization theorem for them, showing that they factor through ¿1. We also present some applications for the case when the range space has some relevant properties, such as the Orlicz or Schur properties. We prove that ¿1 is the only Banach space for which there is a norming bilinear map which equals zero exactly in those couples of functions whose convolution is zero. We also show some examples and applications to generalized convolutions. Erdogan's work was supported by TUBITAK, the Scientific and Technological Research Council of Turkey. Calabuig's work was supported by Ministerio de Economia, Industria y Competitividad (MINECO) grant MTM2014-53009-P. Sanchez Perez's work was supported by MINECO grant MTM2016-77054-C2-1-P. Erdogan, E.; Calabuig, JM.; Sánchez Pérez, EA. (2018). Convolution-continuous bilinear operators acting on Hilbert spaces of integrable functions. Annals of Functional Analysis. 9(2):166-179. https://doi.org/10.1215/20088752-2017-003/1