Multiparameter singular integrals and maximal operators along flat surfaces
Yong-Kum Cho
Chung-Ang University, Seoul, South KoreaSunggeum Hong
Chosun University, Gwangju, South KoreaJoonil Kim
Yonsei University, Seoul, South KoreaChan Woo Yang
Korea University, Seoul, South Korea
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Abstract
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. 1047–1073
DOI 10.4171/RMI/566