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Analysis 9, 323–346 (1989) On weighted Beppo Levi functions—Integral representations and behavior at infinity—
| Content Provider | Semantic Scholar |
|---|---|
| Author | Aikawa, Hiroaki |
| Copyright Year | 2007 |
| Abstract | Abstract: Let 1 < p < ∞ and let w be a weight satisfying the Muckenhoupt Ap condition. A distribution whose partial derivatives of m-th order all belong to the weighted L space L(R, w) is said to be a Beppo Levi function of order m with weight w. The space BLm(L(R, w)) of all Beppo Levi functions includes properly the weighted Sobolev space Wm(L(R, w)) = ∩k=0BLk(L(R, w)). While both the spaces BLm(L(R, w)) and Wm(L(R, w)) have the same local behavior, they have completely different global behavior. We give integral representations of Beppo Levi functions and consider their behavior at infinity. Our results generalize earlier studies of Sobolev [8], Pigolkina [15], Lizorkin [7] and others. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://www.math.sci.hokudai.ac.jp/~aik/research/AikawaPapers/BeppoLevi.pdf |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Courant–Friedrichs–Lewy condition Infinity |
| Content Type | Text |
| Resource Type | Article |
