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 Cet article a éte moissonné depuis la source Numdam

Voir la notice de l'article

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 
@article{ASNSP_2012_5_11_2_341_0,
     author = {Liflyand, Elijah and Tikhonov, Sergey},
     title = {Two-sided weighted {Fourier} inequalities},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {341--362},
     year = {2012},
     publisher = {Scuola Normale Superiore, Pisa},
     volume = {Ser. 5, 11},
     number = {2},
     mrnumber = {3011994},
     zbl = {1278.42006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ASNSP_2012_5_11_2_341_0/}
}
TY  - JOUR
AU  - Liflyand, Elijah
AU  - Tikhonov, Sergey
TI  - Two-sided weighted Fourier inequalities
JO  - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY  - 2012
SP  - 341
EP  - 362
VL  - 11
IS  - 2
PB  - Scuola Normale Superiore, Pisa
UR  - http://geodesic.mathdoc.fr/item/ASNSP_2012_5_11_2_341_0/
LA  - en
ID  - ASNSP_2012_5_11_2_341_0
ER  - 
%0 Journal Article
%A Liflyand, Elijah
%A Tikhonov, Sergey
%T Two-sided weighted Fourier inequalities
%J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
%D 2012
%P 341-362
%V 11
%N 2
%I Scuola Normale Superiore, Pisa
%U http://geodesic.mathdoc.fr/item/ASNSP_2012_5_11_2_341_0/
%G en
%F ASNSP_2012_5_11_2_341_0
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/