Estimates of Fourier transforms in Sobolev spaces
Kolyada, V.
Studia Mathematica, Tome 122 (1997), p. 67-74 / Harvested from The Polish Digital Mathematics Library
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We investigate the Fourier transforms of functions in the Sobolev spaces W1r1,...,rn. It is proved that for any function f∈W1r1,...,rn the Fourier transform f̂ belongs to the Lorentz space Ln/r,1, where r=n(∑j=1n1/rj)-1≤n. Furthermore, we derive from this result that for any mixed derivative Dsf(f∈C0∞,s=(s1,...,sn)) the weighted norm ∥(Dsf)∧∥L1(w)(w(ξ)=|ξ|-n) can be estimated by the sum of L1-norms of all pure derivatives of the same order. This gives an answer to a question posed by A. Pełczyński and M. Wojciechowski.

Publié le : 1997-01-01
EUDML-ID : urn:eudml:doc:216422 
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     title = {Estimates of Fourier transforms in Sobolev spaces},
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     volume = {122},
     year = {1997},
     pages = {67-74},
     zbl = {0896.42008},
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Kolyada, V. Estimates of Fourier transforms in Sobolev spaces. Studia Mathematica, Tome 122 (1997) pp. 67-74. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv125i1p67bwm/

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