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  • 1 Faculty of Science, Ningbo University, Ningbo, Zhejiang, 315211, China
  • | 2 Institute of Mathematics, Zhejiang Sci-Tech University, Hangzhou, Zhejiang, 310018, China
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Abstract

By employing new ideas and techniques, we will refigure out the whole frame of L1-approximation. First, except generalizing the coefficients from monotonicity to a wider condition, Logarithm Rest Bounded Variation condition, we will also drop the prior requirement fL2π but directly consider the sine or cosine series. Secondly, to achieve nontrivial generalizations in complex spaces, we use a one-sided condition with some kind of balance conditions. In addition, a conjecture raised in [9] is disproved in Section 3.

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