Abstract
We establish the L p boundedness of Marcinkiewicz integral operators with kernels in the Hardy space on a compact submanifold of finite type. Previously such boundedness properties were obtained when the submanifold is a sphere. Our result shows that what matters is not the symmetry, but a certain type of curvature property of the submanifold.
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Cheng, L.C. L p boundedness of Marcinkiewicz integrals with H 1 kernels. Acta. Math. Sin.-English Ser. 24, 1031–1038 (2008). https://doi.org/10.1007/s10114-007-5603-4
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DOI: https://doi.org/10.1007/s10114-007-5603-4