| 書目名稱 | Fatou Type Theorems | | 副標題 | Maximal Functions an | | 編輯 | Fausto Biase | | 視頻video | http://file.papertrans.cn/342/341443/341443.mp4 | | 叢書名稱 | Progress in Mathematics | | 圖書封面 |  | | 描述 | A basic principle governing the boundary behaviour of holomorphic func- tions (and harmonic functions) is this: Under certain growth conditions, for almost every point in the boundary of the domain, these functions ad- mit a boundary limit, if we approach the bounda-ry point within certain approach regions. For example, for bounded harmonic functions in the open unit disc, the natural approach regions are nontangential triangles with one vertex in the boundary point, and entirely contained in the disc [Fat06]. In fact, these natural approach regions are optimal, in the sense that convergence will fail if we approach the boundary inside larger regions, having a higher order of contact with the boundary. The first theorem of this sort is due to J. E. Littlewood [Lit27], who proved that if we replace a nontangential region with the rotates of any fixed tangential curve, then convergence fails. In 1984, A. Nagel and E. M. Stein proved that in Euclidean half- spaces (and the unit disc) there are in effect regions of convergence that are not nontangential: These larger approach regions contain tangential sequences (as opposed to tangential curves). The phenomenon discovered by Nagel and | | 出版日期 | Book 1998 | | 關鍵詞 | Fatou Type; Finite; Pseudoconvexity; function; mathematics; maximum; theorem | | 版次 | 1 | | doi | https://doi.org/10.1007/978-1-4612-2310-8 | | isbn_softcover | 978-1-4612-7496-4 | | isbn_ebook | 978-1-4612-2310-8Series ISSN 0743-1643 Series E-ISSN 2296-505X | | issn_series | 0743-1643 | | copyright | Birkh?user 1998 |
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