David studied from 1976 to 1981 at the École normale supérieure, graduating with Agrégation and Diplôme d'études approfondies (DEA).

At the University of Paris-Sud (Paris XI) he received in 1981 his doctoral degree (Thèse du 3ème cycle)[1] and in 1986 his higher doctorate (Thèse d'État) with thesis Noyau de Cauchy et opérateurs de Caldéron-Zygmund supervised by Yves Meyer.

[2] David is known for his research on Hardy spaces and on singular integral equations using the methods of Alberto Calderón.

The T(1) Theorem is of fundamental importance for the theory of singular integral operators of Calderón-Zygmund type.

David also did research on the conjecture of David Mumford and Jayant Shah in image processing and made contributions to the theory of Hardy spaces; the contributions were important for Jones' traveling salesman theorem in