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

C1fLp,wf^Lp,w˜C2fLp,w,w˜(x)=w(1/x)xp-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 : 2018-06-21
Classification:  42A38,  26D15,  46E30
@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},
     publisher = {Scuola Normale Superiore, Pisa},
     volume = {Ser. 5, 11},
     number = {2},
     year = {2012},
     pages = {341-362},
     zbl = {1278.42006},
     mrnumber = {3011994},
     language = {en},
     url = {http://www.numdam.org/item/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, Serie 5, Volume 11 (2012) no. 2, pp. 341-362. http://www.numdam.org/item/ASNSP_2012_5_11_2_341_0/

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