Abstract
In this paper, we introduce certain classes of Calderón–Zygmund operators with kernels of Dini’s type including pseudodifferential operators with smooth symbols. Applying a class of new weight functions, we establish some weighted norm inequalities for certain classes of Calderón–Zygmund operators with kernels of Dini’s type. In addition, new BMO spaces with respect to the class of new weight functions are introduced. Naturally, the pointwise, weighted strong type and endpoint \(L\,\mathrm {log}\,L\) type estimates for the commutators with the new BMO functions are also obtained.
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Acknowledgements
The authors wish to express their sincere thanks to the referees for their careful reading and valuable comments. The second author (JZ) is supported by the National Natural Science Foundation of China (11661075).
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Communicating Editor: E K Narayanan
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Hu, X., Zhou, J. New weighted norm inequalities for Calderón–Zygmund operators with kernels of Dini’s type and their commutators. Proc Math Sci 129, 56 (2019). https://doi.org/10.1007/s12044-019-0505-9
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DOI: https://doi.org/10.1007/s12044-019-0505-9