Rough Marcinkiewicz integrals along certain smooth curves

Bolin MA; Huoxiong WU; Xiating ZHAO

doi:10.1007/s11464-012-0237-y

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Front. Math. China ›› 2012, Vol. 7 ›› Issue (5) : 857-872. DOI: 10.1007/s11464-012-0237-y

RESEARCH ARTICLE

Rough Marcinkiewicz integrals along certain smooth curves

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Abstract

This paper is devoted to the study of the multiple-parameter rough Marcinkiewicz integral operators associated with certain smooth curves. It is shown that the Grafakos-Stefanov type size condition F_α (S^m-1 × S^n-1) of the kernel implies the L^p-boundedness of these Marcinkiewicz integral operators for some $α > 1 / 2$ and $1 + 1 2 α < p < 1 + 2 α$ , which is an essential improvement of certain previous results.

Keywords

Marcinkiewicz integral / rough kernel / smooth curve / LittlewoodPaley theory / Fourier transform estimate

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Bolin MA, Huoxiong WU, Xiating ZHAO. Rough Marcinkiewicz integrals along certain smooth curves. Front Math Chin, 2012, 7(5): 857‒872 https://doi.org/10.1007/s11464-012-0237-y

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