Characterization of the boundedness of the segment multiplier on rearrangement-invariant spaces

2026/07/24 by Miguel F. Barea-Fernández, Ron Kerman, Jan Lang +1
#math.CA #math.FA

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Abstract

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.

Citations

• Estimates for translation invariant operators in Lp spaces

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