Journal article
Strict local inclusion results between spaces of Fourier transforms
Pacific Journal of Mathematics, Vol.99(2), pp.265-270
1982
Abstract
Let G denote a noncompact Hausdorff locally compact abelian group, Γ its character group, and write (Ls,lt)∧ for the space of Fourier transforms of functions in the amalgam (Ls,lt). We show that for 1 ≦ p < q ≦∞ the local inclusion (L1,lp)∧loc ⊂(L∞,lq)∧ is strict, that is, given any nonvoid open subset Ω of Γ there exists f ∈ (L∞,lq) such that f −ĝ does not vanish on Ω for any g ∈ (L1,lp). If in addition G is assumed to be second countable then we show there exists such an f independent of the choice of Ω. Of special interest is the case, included in the above results, where the amalgams (L1,lq), (L∞,lp) are replaced by Lp(G), Lq(G) respectively.
Details
- Title
- Strict local inclusion results between spaces of Fourier transforms
- Authors/Creators
- W. Bloom (Author/Creator)
- Publication Details
- Pacific Journal of Mathematics, Vol.99(2), pp.265-270
- Publisher
- MSP
- Identifiers
- 991005541243107891
- Copyright
- 1982 Pacific Journal of Mathematics
- Murdoch Affiliation
- School of Mathematical and Physical Sciences
- Language
- English
- Resource Type
- Journal article
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- Citation topics
- 9 Mathematics
- 9.50 Applied Statistics & Probability
- 9.50.649 BMO
- Web Of Science research areas
- Mathematics
- ESI research areas
- Mathematics