You are here: Home :: Area NEM :: Mathematics

Loukas Grafakos, Petr Honzik, Dmitry Ryabogin

On the p-independence boundedness property of Calderón-Zygmund theory

For 0 ≦ α < 1 we construct examples of even integrable functions Ω on the unit sphere 𝕊^d-1 with mean value zero satisfying such that the L²-bounded singular integral operator T_Ω given by convolution with the distribution p.v. Ω(x/|x|)|x|^-d is not bounded on L^p(ℝ^d) when . In particular, we construct operators T_Ω that are bounded on L^p exactly when p = 2.

Journal fur die reine und angewandte Mathematik (Crelles Journal), Walter de Gruyter

Print ISSN: 0075-4102
Volume: 2007, 01/2007
Pages: 227 - 234

Show full article (external site)

Show all available items of this journal

 

Area NEM