Hölder Continuous Functions and the Finite Hilbert Transform
✍ Scribed by Susumu Okada; David Elliott
- Publisher
- John Wiley and Sons
- Year
- 2006
- Tongue
- English
- Weight
- 754 KB
- Volume
- 169
- Category
- Article
- ISSN
- 0025-584X
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
## Abstract The boundedness of the finite Hilbert transform operator on certain weighted __L~p~__ spaces is well known. We extend this result to give the boundedness of that operator on certain weighted Sobolev spaces. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Math. Nechr. 149 (1990) and (1.7) respectively, where the parameter 5 tends to 0. n W Z , 5 ) = ( 6 Z -l J I(% + 1) exp (-t2/5) d t , -JI Throughout the paper, we shall write (1.8) @A = I(% + 1) -2f(Z)'+ f ( Z -0 . 2.
As is well-known, there is a close and well-deÿned connection between the notions of Hilbert transform and of conjugate harmonic functions in the context of the complex plane. This holds e.g. in the case of the Hilbert transform on the real line, which is linked to conjugate harmonicity in the upper