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PreprintarXiv licencearXiv

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

  • Miguel F. Barea-Fernández
  • Ron Kerman
  • Jan Lang
  • Javier Soria
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Abstract

Given rearrangement-invariant (r.i.) spaces X and Y, we show that the segment multiplier, the truncated Hilbert transform, and the discrete Hilbert transform (on the associated discretized space) are bounded from X to Y simultaneously. Moreover, when X = Y 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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Cite

BibTeXRIS
BibTeX
@misc{bareafernandez2026characterization,
  title = {{Characterization of the boundedness of the segment multiplier on rearrangement-invariant spaces}},
  author = {Miguel F. Barea-Fernández and Ron Kerman and Jan Lang and Javier Soria},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2607.22277},
  eprint = {2607.22277},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2607.22277},
}
RIS
TY  - UNPB
TI  - Characterization of the boundedness of the segment multiplier on rearrangement-invariant spaces
AU  - Miguel F. Barea-Fernández
AU  - Ron Kerman
AU  - Jan Lang
AU  - Javier Soria
PY  - 2026
DA  - 2026/10/29
PB  - arXiv
DO  - 10.48550/arxiv.2607.22277
UR  - https://arxiv.org/abs/2607.22277
AB  - Given rearrangement-invariant (r.i.) spaces X and Y, we show that the segment multiplier, the truncated Hilbert transform, and the discrete Hilbert transform (on the associated discretized space) are bounded from X to Y simultaneously. Moreover, when X = Y 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.
ER  -