Multiparameter singular integrals and maximal operators along flat surfaces
Yong-Kum ChoChung-Ang University, Seoul, South Korea
Sunggeum HongChosun University, Gwangju, South Korea
Joonil KimYonsei University, Seoul, South Korea
Chan Woo YangKorea University, Seoul, South Korea
We study double Hilbert transforms and maximal functions along surfaces of the form . The boundedness of the maximal operator is obtained if each is a convex increasing and . The double Hilbert transform is bounded in if both 's above are extended as even functions. If is odd, then we need an additional comparability condition on . This result is extended to higher dimensions and the general hyper-surfaces of the form on .
Cite this article
Yong-Kum Cho, Sunggeum Hong, Joonil Kim, Chan Woo Yang, Multiparameter singular integrals and maximal operators along flat surfaces. Rev. Mat. Iberoam. 24 (2008), no. 3, pp. 1047–1073DOI 10.4171/RMI/566