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  • 1 Department of Mathematics, Ningbo University Ningbo, Zhejiang 315211 China Ningbo, Zhejiang 315211 China
  • 2 Institute of Mathematics, Zhejiang Sci-Tech University Xiasha Economic Development Area, Hangzhou, Zhejiang 310018 China Xiasha Economic Development Area, Hangzhou, Zhejiang 310018 China
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Summary  

To verify the universal validity of the ``two-sided'' monotonicity condition introduced in [4], we will apply it to include more classical examples. The present paper selects the Lp convergence case for this purpose. Furthermore, Theorem 3 shows that our improvements are not trivial.

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