Singular integrals generated by zonal measures

Authors
Ryabogin, D Rubin, B
Citation
D. Ryabogin et B. Rubin, Singular integrals generated by zonal measures, P AM MATH S, 130(3), 2001, pp. 745-751
Citations number
12
Categorie Soggetti
Mathematics
Journal title
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
ISSN journal
00029939 → ACNP
Volume
130
Issue
3
Year of publication
2001
Pages
745 - 751
Database
ISI
SICI code
0002-9939(2001)130:3<745:SIGBZM>2.0.ZU;2-J
Abstract
We study L-p-mapping properties of the rough singular integral operator T(n u)f(x) = integral (infinity)(0) dr/r integral (Sigma n-1) f(x-r theta )d nu (theta )depending on a finite Borel measure nu on the unit sphere Sigma (n- 1) in R-n. It is shown that the conditions sup (\ xi \ = 1) integral (Sigma n-1) log (1/\ theta . xi \ )d \v \(theta) < <infinity>, nu(Sigma (n-1)) = 0 imply the L-p-boundedness of T-nu for all 1 < p < infinity provided that n >2 and nu is zonal.