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Polydiscs and Nontangential Limits
| Content Provider | Scilit |
|---|---|
| Author | Gowrisankaran, Kohur |
| Copyright Year | 1992 |
| Description | A well-known result states that for all bounded $n$-harmonic functions on the polydisc ${\mathbb {D}^n}$ the nontangential limits exist for (Lebesgue) almost every element of the $n$-torus. In this paper it is shown that a similar result is not in general valid for bounded quotients of two positive $n$-harmonic functions. Necessary and sufficient conditions on a $n$-harmonic function $u > 0$ are given to ensure the existence "almost everywhere" of the nontangential limits of the quotients $w/u$ in the case (i) for all $n$-harmonic functions $w$ such that $w/u$ is bounded and in the case (ii) for all $n$-harmonic functions $w$ that are $u$-quasi-bounded.' |
| Related Links | https://www.ams.org/proc/1992-115-04/S0002-9939-1992-1113640-7/S0002-9939-1992-1113640-7.pdf |
| Ending Page | 984 |
| Page Count | 8 |
| Starting Page | 977 |
| ISSN | 00029939 |
| e-ISSN | 10886826 |
| DOI | 10.2307/2159343 |
| Journal | Proceedings of the American Mathematical Society |
| Issue Number | 4 |
| Volume Number | 115 |
| Language | English |
| Publisher | Duke University Press |
| Publisher Date | 1992-08-01 |
| Access Restriction | Open |
| Subject Keyword | Logic Functions Nontangential Limits Polydiscs Harmonic W/u Lebesgue Quasi Mathbb Torus |
| Content Type | Text |
| Resource Type | Article |
| Subject | Applied Mathematics |
