Work

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

Year: 2026

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2607.22277

Authors: Barea-Fernández, Miguel F., Kerman, Ron, Lang, Jan, Soria, Javier

Language: English

Topic: Advanced Banach Space Theory

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Ministerio de Ciencia, Innovación y Universidades, Agencia Estatal de Investigación

Awards: G2262748287, G3480869486, G3824717177, G4233400527, G425668148, G4526231891, G4584367659, G5635532810, G6390997812, G6731524417, G7084143925, G717256432, G7863371703, G804350674, G8497050386

OpenAlex ID: W7171373669

Cites:

Cited by: 1

Related to: 10