Geodesic
Two-sided weighted Fourier inequalities
Liflyand, Elijah1  ; Tikhonov, Sergey2 
1 Department of Mathematics Bar-Ilan University 52900 Ramat-Gan, Israel
2 ICREA and Centre de Recerca Matemàtica Apartat 50 08193 Bellaterra Barcelona, Spain
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 11 (2012) no. 2, pp. 341-362

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Fourier transform estimates for ∥f ^∥ L q,w ˜ via ∥f∥ L p,w from above and from below are studied. For p=q, equivalence results, i.e.,

C 1 ∥f∥ L p,w ≤∥f ^∥ L p,w ˜ ≤C 2 ∥f∥ L p,w ,w ˜(x)=w(1/x)x p-2 ,1≤p<∞,

are shown to be valid for functions from certain classes under the Muckenhoupt conditions: w∈A p or w∈A 2p . Sharpness of these conditions is proved.

Publié le :
Classification : 42A38, 26D15, 46E30

Liflyand, Elijah 1 ; Tikhonov, Sergey 2

1 Department of Mathematics Bar-Ilan University 52900 Ramat-Gan, Israel
2 ICREA and Centre de Recerca Matemàtica Apartat 50 08193 Bellaterra Barcelona, Spain 
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     title = {Two-sided weighted {Fourier} inequalities},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {341--362},
     publisher = {Scuola Normale Superiore, Pisa},
     volume = {Ser. 5, 11},
     number = {2},
     year = {2012},
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Liflyand, Elijah; Tikhonov, Sergey. Two-sided weighted Fourier inequalities. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 11 (2012) no. 2, pp. 341-362. http://geodesic.mathdoc.fr/item/ASNSP_2012_5_11_2_341_0/