Welcome to the new version of CaltechAUTHORS. Login is currently restricted to library staff. If you notice any issues, please email coda@library.caltech.edu
Published 1973 | public
Journal Article Open

A Hausdorff-Young theorem for rearrangement-invariant spaces

Bennett, Colin

Abstract

The classical Hausdorff-Young theorem is extended to the setting of rearrangement-invariant spaces. More precisely, if 1 <_ p <_ 2, p[-1] + q[-1] = 1, and if X is a rearrangement-invariant space on the circle T with indices equal to p[-1], it is shown that there is a rearrangement-invariant space X on the integers Z with indices equal to q[-1] such that the Fourier transform is a bounded linear operator from X into X. Conversely, for any rearrangement-invariant space Y on Z with indices equal to q[-1], 2 < q <__ oo, there is a rearrangement-invariant space Y on T with indices equal to p[-1] such that J is bounded from Y into Y. Analogous results for other groups are indicated and examples are discussed when X is L[p] or a Lorentz space L[pr].

Files

BENpjm73.pdf
Files (1.5 MB)
Name Size Download all
md5:81a989a8d5e6e44bfad71e1a9ecc949a
1.5 MB Preview Download

Additional details

Created:
August 22, 2023
Modified:
October 13, 2023