Estimates Lʳ-Lˢ for solutions of the ∂ equation in strictly pseudo convex domains in Cⁿ.

الأصل · EN

We prove estimates for solutions of the ∂ u=ω equation in a strictly pseudo convex domain Ω in Cⁿ. For instance if the (p,q) current ω has its coefficients in Lʳ(Ω) with 1≤ r<2(n+1) then there is a solution u in Lˢ(Ω) with 1/s=1/r-1/2(n+1). We also have BMO and Lipschitz estimates for r≥ 2(n+1). These results were already done by S. Krantz in the case of (0,1) forms and just for the Lʳ-Lˢ part by L. Ma and S. Vassiliadou for general (p,q) forms. To get the complete result we propose another approach, based on Carleson measures of order α and on the subordination lemma.