HARDY-SOBOLEV SPACES OF COMPLEX TANGENTIAL DERIVATIVES OF HOLOMORPHIC FUNCTIONS IN DOMAINS OF FINITE TYPE

Sandrine Grellier (1)

1 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans

In this paper, we prove Fefferman-Stein like characterizations of Hardy-Sobolev spaces of complex tangential derivatives of holomorphic functions in domains of finite type in Cn. We also study the relationship between these complex tangential Hardy-Sobolev spaces and the usual ones. We also obtain partial results on domains not necessarily of finite type.

Mots clés: domains of finite type; Hardy spaces; Hardy-Sobolev spaces; maximal functions; area integrals; Fefferman-Stein Theory; complex tangential derivatives

Domaines: Variables complexes [math.CV]

Sandrine Grellier. HARDY-SOBOLEV SPACES OF COMPLEX TANGENTIAL DERIVATIVES OF HOLOMORPHIC FUNCTIONS IN DOMAINS OF FINITE TYPE. Mathematica Scandinavica, 2002, 90, pp.232-250. ⟨hal-00077115⟩