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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 L p convergence case for this purpose. Furthermore, Theorem 3 shows that our improvements are not trivial.

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remark on “two-sidedmonotonicity condition: an application to L p convergence, Acta Math. Hungar. 113 (2006), no. 1–2, 159–169. MR 2007f :42006 Le R. J. A remark on

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