Geodesic
On a Stein And Weiss Property of the Conjugate Function
Canadian journal of mathematics, Tome 42 (1990) no. 1, pp. 109-125

Voir la notice de l'article provenant de la source Cambridge University Press

(1.1) The conjugate function on locally compact abelian groups. Let G be a locally compact abelian group with character group Ĝ. Let μ denote a Haar measure on G such that μ(G) = 1 if G is compact. (Unless stated otherwise, all the measures referred to below are Haar measures on the underlying groups.) Suppose that Ĝ contains a measurable order P: P + P ⊆P; PU(-P)= Ĝ; and P⋂(—P) ={0}. For ƒ in L2(G), the conjugate function of f (with respect to the order P) is the function whose Fourier transform satisfies the identity for almost all χ in Ĝ, where sgnP(χ)= 0, 1, or —1, according as χ =0, χ ∈ P\\{0}, or χ ∈ (—P)\{0}. 
Asmar, Nakhlé. On a Stein And Weiss Property of the Conjugate Function. Canadian journal of mathematics, Tome 42 (1990) no. 1, pp. 109-125. doi: 10.4153/CJM-1990-007-3
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