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Volume 120, 2008, pp. 127–138
DOI: 10.4171/RSMUP/120-7

Hölder Type Estimates for the $\overline\partial$-Equation in Strongly Pseudoconvex Domains

Heungju Ahn[1], Hong Rae Cho[2] and Jong-Do Park[3]

(1) National Institute for Mathematical Sciences, Tower Koreana, 628 Daeduk-Boulevard, 305-340, Daejeon, Republic of Korea
(2) Department of Mathematics, Pusan National University, Geumjeong-gu, 609-735, Busan, Republic of Korea
(3) Department of Mathematics, Pohang University of Science and Technology, San 31, Hyoja-dong, Namgu, Pohang, 790-784, Kyungbuk, Republic of Korea

In this paper we generalize the Hölder space with a majorant function, define its order, and prove the existence and regularity for the solutions of the Cauchy-Riemann equation in the generalized Hölder space over a bounded strongly pseudoconvex domain.

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Ahn Heungju, Cho Hong Rae, Park Jong-Do: Hölder Type Estimates for the $\overline\partial$-Equation in Strongly Pseudoconvex Domains. Rend. Sem. Mat. Univ. Padova 120 (2008), 127-138. doi: 10.4171/RSMUP/120-7