Geodesic
Weighted estimates of the Fourier transformation
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 23, Tome 222 (1995), pp. 151-162 
O. G. Parfenov. Weighted estimates of the Fourier transformation. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 23, Tome 222 (1995), pp. 151-162. http://geodesic.mathdoc.fr/item/ZNSL_1995_222_a5/
@article{ZNSL_1995_222_a5,
     author = {O. G. Parfenov},
     title = {Weighted estimates of the {Fourier} transformation},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {151--162},
     year = {1995},
     volume = {222},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1995_222_a5/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

The Fourier transformation is regarded as an operator from $\mathcal L_2(-\pi,\pi)$ to $\mathcal L_2(\mathbb R,\mu)$, where $\mu$ is a measure on the real axis $\mathbb R$. Some criteria are obtained for this operator to be bounded or compact, or to belong to some symmetrically normed ideal with the domination property. These results can be viewed as a description of the Carleson measures for the Paley–Wiener space of entire functions. Bibliography: 15 titles.