Uniform estimates for the Cauchy-Riemann equation on q-convex wedges
Annales de l'Institut Fourier, Volume 43 (1993) no. 2, p. 383-436

We study the ¯-equation with Hölder estimates in q-convex wedges of n by means of integral formulas. If D n is defined by some inequalities {ρ i 0}, where the real hypersurfaces {ρ i =0} are transversal and any nonzero linear combination with nonnegative coefficients of the Levi form of the ρ i ’s have at least (q+1) positive eigenvalues, we solve the equation ¯f=g for each continuous (n,r)-closed form g in D, n-qrn, with the following estimates: if d denotes the distance to the boundary of D and if d β g is bounded, then for all ε>0, f is Hölder continuous with exponent 1/2-β-ε if 0β<1/2 and d β+ε-1/2 f is bounded if 1/2β<1.

Dans ce travail on résoud l’équation de Cauchy-Riemann avec des estimées höldériennes dans une intersection de domaines q-convexes. Plus précisément si D n est défini par des inégalités {ρ i 0}, où les hypersurfaces réelles {ρ i 0} sont transverses et les combinaisons linéaires non nulles à coefficients positifs des formes de Levi des ρ i ont toutes au moins (q+1) valeurs propres strictement positives, on résoud, en utilisant des formules intégrales, l’équation ¯f=g, où g est une (n,r)-forme différentielle continue, ¯-fermée dans D,n-qrn, avec les estimées suivantes : si d désigne la distance au bord de D, et si d β g est bornée alors pour tout ε>0, f est höldérienne d’ordre 1/2-β-ε si 0β<1/2 et d β+ε-1/2 f est bornée si 1/2β<1.

@article{AIF_1993__43_2_383_0,
     author = {Laurent-Thi\'ebaut, Christine and Leiterer, Jurgen},
     title = {Uniform estimates for the Cauchy-Riemann equation on $q$-convex wedges},
     journal = {Annales de l'Institut Fourier},
     publisher = {Imprimerie Louis-Jean},
     address = {Gap},
     volume = {43},
     number = {2},
     year = {1993},
     pages = {383-436},
     doi = {10.5802/aif.1338},
     zbl = {0782.32014},
     mrnumber = {95a:32025},
     language = {en},
     url = {http://www.numdam.org/item/AIF_1993__43_2_383_0}
}
Laurent-Thiébaut, Christine; Leiterer, Jurgen. Uniform estimates for the Cauchy-Riemann equation on $q$-convex wedges. Annales de l'Institut Fourier, Volume 43 (1993) no. 2, pp. 383-436. doi : 10.5802/aif.1338. http://www.numdam.org/item/AIF_1993__43_2_383_0/

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