期刊名称：Proceedings of the National Academy of Sciences
印刷版ISSN：0027-8424
电子版ISSN：1091-6490
出版年度：1975
卷号：72
期号：9
页码：3287-3289
DOI：10.1073/pnas.72.9.3287
语种：English
出版社：The National Academy of Sciences of the United States of America
摘要：We find the necessary and sufficient conditions for the local solvability of Lewy's equation, ([unk]/[unk]z +[i] z [unk]/[unk]t) u = f. If R3 is realized as the boundary of the generalized "upper-half-space" in C2, then the conditions are, near a point P [unk] R3, the analytic continuability of the Cauchy-Szego integral of f past P. In case the sufficient condition is satisfied, solutions are found that satisfy optimal regularity properties. Various generalizations are also given.
关键词：Cauchy-Szegö integral ; Heisenberg group ; holomorphic functions
