Two-sided weighted Fourier inequalities
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 11 (2012) no. 2, pp. 341-362.

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 ,1p<,

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

Published online:
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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Liflyand, Elijah; Tikhonov, Sergey. Two-sided weighted Fourier inequalities. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 11 (2012) no. 2, pp. 341-362. http://archive.numdam.org/item/ASNSP_2012_5_11_2_341_0/

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