The Fourier transform in weighted Lorentz spaces

G. Sinnamon
2003 Publicacions matemàtiques  
Necessary conditions and sufficient conditions on weights u and w are given for the Fourier transform F to be bounded as a map between the Lorentz spaces Γq(w) and Λp(u). This may be viewed as a weighted extension of a result of Jodeit and Torchinsky on operators of type (1, ∞) and (2, 2). In the case 0 < p ≤ 2 = q, the necessary and sufficient conditions are equivalent and give a simple weight condition which is equivalent to F : Γ 2 (w) → Λp(u) and also to F : Γ 2 (w) → Γp(u).
doi:10.5565/publmat_47103_01 fatcat:63vtpvjfvbc65ian6b6mzgdlmu