Comptes Rendus
Analyse complexe, Équations aux dérivées partielles
On the canonical solution of ¯ on polydisks
Comptes Rendus. Mathématique, Volume 358 (2020) no. 5, pp. 523-528.

We observe that the recent result of Chen–McNeal [6] implies that the canonical solution operator satisfies Sobolev estimates with a loss of n-2 derivatives on the polydisk Δ n and particularly is exact regular on Δ 2 .

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DOI : 10.5802/crmath.51
Muzhi Jin 1 ; Yuan Yuan 1

1 Department of Mathematics, Syracuse University, Syracuse, NY 13244, USA
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits
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     title = {On the canonical solution of $\protect \,\protect \,\protect \overline{\protect \!\partial }$ on polydisks},
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Muzhi Jin; Yuan Yuan. On the canonical solution of $\protect \,\protect \,\protect \overline{\protect \!\partial }$ on polydisks. Comptes Rendus. Mathématique, Volume 358 (2020) no. 5, pp. 523-528. doi : 10.5802/crmath.51. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.51/

[1] Lars V. Ahlfors Lectures on quasiconformal mappings, University Lecture Series, 38, American Mathematical Society, 2006 (with supplemental chapters by C. J. Earle, I. Kra, M. Shishikura and J. H. Hubbard) | MR | Zbl

[2] Harold P. Boas Holomorphic reproducing kernels in Reinhardt domains, Pac. J. Math., Volume 112 (1984) no. 2, pp. 273-292 | DOI | MR | Zbl

[3] Debraj Chakrabarti; Christine Laurent-Thiébaut; Mei-Chi Shaw On the L 2 -Dolbeault cohomology of annuli, Indiana Univ. Math. J., Volume 67 (2018) no. 2, pp. 831-857 | DOI | MR | Zbl

[4] Debraj Chakrabarti; Mei-Chi Shaw The Cauchy–Riemann equations on product domains, Math. Ann., Volume 349 (2011) no. 4, pp. 977-998 | DOI | MR | Zbl

[5] Liwei Chen Weighted Sobolev regularity of the Bergman projection on the Hartogs triangle, Pac. J. Math., Volume 288 (2017) no. 2, pp. 307-318 | DOI | MR | Zbl

[6] Liwei Chen; Jeffery D. McNeal Product domains, Multi-Cauchy transforms, and the ¯ equation, Adv. Math., Volume 360 (2020), 106930, 42 pages | MR | Zbl

[7] Liwei Chen; Jeffery D. McNeal A solution operator for ¯ on the Hartogs triangle and L p estimates, Math. Ann., Volume 376 (2020) no. 1-2, pp. 407-430 | DOI | MR | Zbl

[8] Luke D. Edholm; Jeffery D. McNeal Sobolev mapping of some holomorphic projections, J. Geom. Anal., Volume 30 (2020) no. 2, pp. 1293-1311 | DOI | MR | Zbl

[9] Siqi Fu; Emil J. Straube Compactness of the ¯-Neumann problem on convex domains, J. Funct. Anal., Volume 159 (1998) no. 2, pp. 629-641 | MR | Zbl

[10] Olli Lehto; K. I. Virtanen Quasiconformal mappings in the plane. Translated from the German by K. W. Lucas, Grundlehren der Mathematischen Wissenschaften, 126, Springer, 1973 | Zbl

[11] Martí Prats; Xavier Tolsa A T(P) theorem for Sobolev spaces on domains, J. Funct. Anal., Volume 268 (2015) no. 10, pp. 2946-2989 | DOI | MR | Zbl

[12] Mei-Chi Shaw The Hartogs triangle in complex analysis, Geometry and topology of submanifolds and currents (Contemporary Mathematics), Volume 646, American Mathematical Society, 2015, pp. 105-115 | MR | Zbl

[13] Emil J. Straube Exact regularity of Bergman, Szegö and Sobolev space projections in nonpseudoconvex domains, Math. Z., Volume 192 (1986) no. 1, pp. 117-128 | DOI | Zbl

[14] Emil J. Straube Lectures on the L 2 -Sobolev theory of the ¯-Neumann problem, ESI Lectures in Mathematics and Physics, 7, European Mathematical Society, 2010 | Zbl

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