Optimal Lipschitz estimates for the ∂ ¯ equation on a class of convex domains
Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 12 (2003) no. 2, pp. 179-243. 
@article{AFST_2003_6_12_2_179_0,
     author = {Nguy\^en, Vi\^et Anh and Youssfi, El Hassan},
     title = {Optimal {Lipschitz} estimates for the $\overline{\partial }$ equation on a class of convex domains},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {179--243},
     publisher = {Universit\'e Paul Sabatier, Institut de math\'ematiques},
     address = {Toulouse},
     volume = {Ser. 6, 12},
     number = {2},
     year = {2003},
     mrnumber = {2123255},
     language = {en},
     url = {http://archive.numdam.org/item/AFST_2003_6_12_2_179_0/}
}
TY  - JOUR
AU  - Nguyên, Viêt Anh
AU  - Youssfi, El Hassan
TI  - Optimal Lipschitz estimates for the $\overline{\partial }$ equation on a class of convex domains
JO  - Annales de la Faculté des sciences de Toulouse : Mathématiques
PY  - 2003
SP  - 179
EP  - 243
VL  - 12
IS  - 2
PB  - Université Paul Sabatier, Institut de mathématiques
PP  - Toulouse
UR  - http://archive.numdam.org/item/AFST_2003_6_12_2_179_0/
LA  - en
ID  - AFST_2003_6_12_2_179_0
ER  - 
%0 Journal Article
%A Nguyên, Viêt Anh
%A Youssfi, El Hassan
%T Optimal Lipschitz estimates for the $\overline{\partial }$ equation on a class of convex domains
%J Annales de la Faculté des sciences de Toulouse : Mathématiques
%D 2003
%P 179-243
%V 12
%N 2
%I Université Paul Sabatier, Institut de mathématiques
%C Toulouse
%U http://archive.numdam.org/item/AFST_2003_6_12_2_179_0/
%G en
%F AFST_2003_6_12_2_179_0
Nguyên, Viêt Anh; Youssfi, El Hassan. Optimal Lipschitz estimates for the $\overline{\partial }$ equation on a class of convex domains. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 12 (2003) no. 2, pp. 179-243. http://archive.numdam.org/item/AFST_2003_6_12_2_179_0/

[1] Berndtsson ( B. ). - A formula for interpolation and division in Cn, Math. Ann. 263, p. 399-418 (1983). | MR | Zbl

[2] Bonami (A. ) and Charpentier (P.). - Solutions de l'équation ∂ et zéros de la classe de Nevanlinna dans certains domaines faiblement pseudo-convexes , Ann. Inst. Fourier. 32(4), p. 53-89 (1982). | Numdam | MR | Zbl

[3] Charpentier ( P.). - Formules explicites pour les solutions minimales de l'équation ∂u = f dans la boule et dans le polydisque de Cn, Ann. Inst. Fourier. 30(4), p. 121-154 (1980). | Numdam | MR | Zbl

[4] Chen (Z.) , Krantz ( S.G.) and Ma (D.). - Optimal Lp estimates for the ∂ equation on complex ellipsoids in Cn, Manuscripta math. 80, p. 131-149 (1993). | MR | Zbl

[5] Cumenge (A. ). - Estimées Lipschitz optimales dans les convexes de type fini, C. R. Acad. Sci. Paris 325, p. 1077-1080 (1997). | MR | Zbl

[6] Cumenge (A. ).- Sharp estimates for ∂ on convex domains of finite type, Ark. Mat. 39, p. 1-25 (2001). | MR | Zbl

[7] Diederich ( K.), Fischer (B.) and Fornæss (J.E.). - Hõlder estimates on convex domains of finite type, Math. Z. 232, p. 43-61 (1999). | Zbl

[8] Fischer (B. ) . - Lp estimates on convex domains of finite type, Math. Z. 236, p. 401-418 (2001). | MR | Zbl

[9] Greiner (P. ) and Stein (E.). - "Estimates for the ∂-Neumann problem", Mathematical Notes 19, Princeton University Press, (1977 ). | MR | Zbl

[10] Hefer (T. ).- Hõlder and LP estimates for ∂ on convex domains of finite type depending on Catlin's multitype, Math. Z. 242, p. 367-398 (2002). | Zbl

[11] Krantz (S.G. ). - Optimal Lipschitz and LP regularity for the equation ∂u = f on strongly pseudo-convex domains, Math. Annalen. 219, p. 233-260 (1976). | MR | Zbl

[12] Krantz (S.G. ). - Estimates for integral kernels of mixed type, fractional integration operators, and optimal estimates for the ∂ operator, Manuscripta math. 30, p. 21-52 (1979). | MR | Zbl

[13] Krantz (S.G. ). - Characterizations of various domains of holomorphy via ∂ estimates and applications to a problem of Kohn, Illinois. Journal Math. 23(2), p. 267-285 (1979). | MR | Zbl

[14] Lelong (P. ) and Gruman (L.). - "Entire functions of several complex variables", Grundlehren der Mathematischen Wissenschaften 282, Springer-Verlag, (1986). | MR | Zbl

[15] Mengotti ( G.) and Youssfi (E.H.). - The weighted Bergman projection and related theory on the minimal ball, Bull. Sci. math. 123, p. 501-525 (1999). | MR | Zbl

[16] Rudin (W. ). - "Function theory in the unit ball of Cn ", Grundlehren der Mathematischen Wissenschaften 241, Springer-Verlag, New York-Berlin, 1980. | MR | Zbl

[17] Viêt Anh ( N.).- Fatou and Korányi-Vági type theorems on the minimal balls, Publ. Mat. 46, 49-75 (2002). | MR | Zbl

[18] Viêt Anh ( N.) and Youssfi (E.H.). - Lipschitz estimates for the ∂-equation on the minimal ball, Michigan Math. J. 49, p. 299-323 (2001). | MR | Zbl

[19] Viêt Anh ( N.) and Youssfi (E.H.). - Estimations Lipschitziennes optimales pour l'équation ∂ dans une classe de domaines convexes, C. R. Acad. Sci. Paris t. 332, Série I, p. 1065-1070 (2001). | MR | Zbl

[20] Youssfi ( E.H.). - Proper holomorphic liftings and new formulas for the Bergman and Szegõ kernels, Stud. Math. 152, 161-186 (2002). | Zbl