AI 中文总结
研究重排不变空间上分段乘子等变换的有界性，通过一对博伊德型指标刻画其有界性，还展示了分段乘子有界但非截断希尔伯特变换无界的重排不变空间。
AI 中文摘要
给定一个重排不变（r.i.）空间X，我们证明了分段乘子、截断希尔伯特变换和（在相关离散空间上的）离散希尔伯特变换在X上同时有界。此外，这种有界性由一对博伊德型指标的条件来刻画。我们还展示了一个r.i.空间，其中分段乘子有界而（非截断的）希尔伯特变换无界。
英文摘要
Given a rearrangement-invariant (r.i.) space X, we show that the segment multiplier, the truncated Hilbert transform, and the discrete Hilbert transform (on the associated discretized space) are bounded on X simultaneously. Moreover, this boundedness is characterized by a condition on a pair of Boyd-type indices. We also exhibit an r.i. space on which the segment multiplier is bounded while the (non-truncated) Hilbert transform fails to be bounded.
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