Oscillation and variation for Riesz transform in setting of Bessel operators on H1 and BMO |
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Authors: | Xiaona CUI Jing ZHANG |
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Institution: | 1. College of Mathematics and Information Science, Henan Normal University, Xinxiang 453007, China2. School of Mathematics and Statistics, Yili Normal University, Yining 835000, China |
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Abstract: | Let and let the Bessel operator defined on . We show that the oscillation and -variation operators of the Riesz transform associated with are bounded on BMO, where and . Moreover, we construct a -atom as a counterexample to show that the oscillation and -variation operators of are not bounded from to . Finally, we prove that the oscillation and the -variation operators for the smooth truncations associated with Bessel operators are bounded from to . |
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Keywords: | Oscillation operator variation operator Bessel operator |
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