Journal of Mathematical Sciences

, Volume 87, Issue 5, pp 3878–3885

Weighted estimates of the fourier transformation

  • O. G. Parfenov

DOI: 10.1007/BF02355829

Cite this article as:
Parfenov, O.G. J Math Sci (1997) 87: 3878. doi:10.1007/BF02355829


The Fourier transformation is regarded as an operator fromL2(−π, π) toL2(ℝ,µ), where μ is a measure on the real axis 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.

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© Plenum Publishing Corporation 1997

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  • O. G. Parfenov

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