Very recently,Yu,Le and Zhou introduced the so called Δ*B1 and Δ*B2 conditions,which are generalizations of the monotone condition.By applying these two new conditions,the author essentially generalizes the classical results of Chen on the necessary and sufficient conditions of the Lp integrability of trigonometric series.In fact,the present paper gives the first result on the necessary and sufficient conditions of the Lp integrability of trigonometric series,where coefficients may have diffierent signs.
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