| Weighted Variation Inequalities for Singular Integrals and Commutators in Rearrangement Invariant Banach and Quasi-Banach Spaces |
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| 作者姓名： | Jia Wei TAN Qing Ying XUE |
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| 作者单位： | School of Mathematical Sciences, Beijing Normal University,Laboratory of Mathematics and Complex Systems, Ministry of Education |
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| 基金项目： | supported partly by the National Key R&D Program of China (Grant No.2020YFA0712900)；;NNSF of China (Grant Nos. 11871101, 12271041)； |
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| 摘 要： | In order to study the boundedness of some operators in general function spaces which include Lorentz spaces and Orlicz spaces as special examples,Lorentz introduced a new space called rearrangement invariant Banach function spaces,denoted by RIBFS.It is shown in this paper that variation operators of singular integrals and their commutators are bounded on RIBFS whenever the kernels satisfy the Lr-H?rmander conditions.Moreover,we obtain some quantitative weighted bounds in the quasi-Ba...
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