Bennett, Colin (1973) A Hausdorff-Young theorem for rearrangement-invariant spaces. Pacific Journal of Mathematics, 47 (2). pp. 311-328. ISSN 0030-8730. http://resolver.caltech.edu/CaltechAUTHORS:BENpjm73
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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].
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|Deposited By:||Tony Diaz|
|Deposited On:||18 Aug 2005|
|Last Modified:||26 Dec 2012 08:40|
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