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Rough Marcinkiewicz integrals with mixed homogeneity on product spaces

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Abstract

In this paper, the parabolic Marcinkiewicz integral operators on the product spaces ℝm × ℝn(m, n ≥ 2) are studied. The L p-boundedness for such operators are established under rather weak size conditions of the kernels, which essentially improve or extend certain previous results.

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Correspondence to Huo Xiong Wu.

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Supported by National Natural Science Foundation of China (Grant No. 11071200) and Natural Science Foundation of Fujian Province (Grant No. 2010J01013)

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Liu, F., Wu, H.X. Rough Marcinkiewicz integrals with mixed homogeneity on product spaces. Acta. Math. Sin.-English Ser. 29, 1231–1244 (2013). https://doi.org/10.1007/s10114-013-1675-5

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  • DOI: https://doi.org/10.1007/s10114-013-1675-5

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