Shanzhen Lu, Huixia Mo, "Boundedness of higher-order Marcinkiewicz-Type integrals", International Journal of Mathematics and Mathematical Sciences, vol. 2006, Article ID 031705, 21 pages, 2006. https://doi.org/10.1155/IJMMS/2006/31705
Boundedness of higher-order Marcinkiewicz-Type integrals
Let be a function with derivatives of order and . The authors in the paper proved that if is homogeneous of degree zero and satisfies a vanishing condition, then both the higher-order Marcinkiewicz-type integral and its variation are bounded from to and from to , where and . Furthermore, if satisfies some kind of -Dini condition, then both and are bounded on Hardy spaces, and is also bounded from to certain Triebel-Lizorkin space.
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