Abstract
We prove weighted q-variation inequalities with 2 < q < ∞ for sharp truncations of singular integral operators in higher dimensions. The vector-valued extensions of these inequalities are also given. Parallel results are proven for differential operators.
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Acknowledgements
This work was supported by National Natural Science Foundation of China (Grant Nos. 11671308 and 11431011) and Ministerio de Economía y Competitividad/al Fondo Europeo de Desarrollo Regional (Grant No. MTM2015-66157-C2-1-P). The authors are very grateful to Guixiang Hong for helping us to fix up the proof of the weak type (1; 1) inequality in Theorem 1.6.
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Ma, T., Torrea, J.L. & Xu, Q. Weighted variation inequalities for differential operators and singular integrals in higher dimensions. Sci. China Math. 60, 1419–1442 (2017). https://doi.org/10.1007/s11425-016-9012-7
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DOI: https://doi.org/10.1007/s11425-016-9012-7
Keywords
- variation inequalities
- A p weights
- differential operators
- singular integrals
- vector-valued variation inequalities