Boundedness of Oscillatory Hyper-Hilbert Transform along Curves on Sobolev Spaces
Joint Authors
Source
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-5, 5 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-05-19
Country of Publication
Egypt
No. of Pages
5
Main Subjects
Abstract EN
The oscillatory hyper-Hilbert transform along curves is of the following form: Hn,α,βf(x)=∫01f(x-Γ(t))eit-βt-1-αdt, where α≥0, β≥0, and Γ(t)=(tp1,tp2,…,tpn).
The study on this operator is motivated by the hyper-Hilbert transform and the strongly singular integrals.
The Lp bounds for Hn,α,β have been given by Chen et al.
(2008 and 2010).
In this paper, for some α, β, and p, the boundedness of Hn,α,β on Sobolev spaces Lsp(Rn) and the boundedness of this operator from Ls2(Rn) to L2(Rn) are obtained.
American Psychological Association (APA)
Li, Jun& Gao, Guilian. 2014. Boundedness of Oscillatory Hyper-Hilbert Transform along Curves on Sobolev Spaces. Journal of Function Spaces،Vol. 2014, no. 2014, pp.1-5.
https://search.emarefa.net/detail/BIM-1040675
Modern Language Association (MLA)
Li, Jun& Gao, Guilian. Boundedness of Oscillatory Hyper-Hilbert Transform along Curves on Sobolev Spaces. Journal of Function Spaces No. 2014 (2014), pp.1-5.
https://search.emarefa.net/detail/BIM-1040675
American Medical Association (AMA)
Li, Jun& Gao, Guilian. Boundedness of Oscillatory Hyper-Hilbert Transform along Curves on Sobolev Spaces. Journal of Function Spaces. 2014. Vol. 2014, no. 2014, pp.1-5.
https://search.emarefa.net/detail/BIM-1040675
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1040675