论文信息 - Optimal H\"{o}lder regularity for the $\bar\partial$ problem on product domains in $\mathbb C^2$ - 字舞流文

Optimal H\"{o}lder regularity for the $\bar\partial$ problem on product domains in $\mathbb C^2$

The note concerns the ∂̄ problem on product domains in C2. We show that there exists a bounded solution operator from C into itself, k ∈ Z+∪{0}, 0 < α < 1. The regularity result is optimal in view of an example of Stein-Kerzman.

[1] J. McNeal,et al. Product domains, multi-Cauchy transforms, and the ∂¯ equation , 2019, Advances in Mathematics.

[2] H. Grauert,et al. Das Ramirezsche Integral Und Die Lösung Der Gleichung ϑf= α Im Bereich Der Beschräankten Formen , 1970 .

[3] K. Diederich,et al. Hölder estimates on convex domains of finite type , 1999 .

[4] A. Tumanov. On the propagation of extendibility of CR functions , 1996 .

[5] I. Lieb,et al. Lösungsoperatoren für den Cauchy-Riemann-Komplex mitC1k-abschätzungen , 1980 .

[6] Cauchy singular integral operator with parameters in Log-Hölder spaces , 2020, Journal d'Analyse Mathématique.

[7] F. Sauvigny,et al. Generalized Analytic Functions , 2012 .

[8] A. Nijenhuis,et al. SOME INTEGRATION PROBLEMS IN ALMOST-COMPLEX AND COMPLEX MANIFOLDS , 1963 .

[9] Yuan Yuan. On the canonical solution of ∂ on polydisks , 2020 .

[10] A. Skubachevskii,et al. EXACT HÖLDER ESTIMATES FOR THE SOLUTIONS OF THE -EQUATION , 2017 .

[11] P. Bassanini,et al. Elliptic Partial Differential Equations of Second Order , 1997 .