Geodesic
$L_p$-Inequalities for Differences and Derivatives of Positive Order for Functions with Spectrum in the Ball or Spherical Layer
Matematičeskie zametki, Tome 95 (2014) no. 3, pp. 433-444.

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We prove inequalities of Riesz, Bernstein, and Bohr–Favard type in the metric of the spaces $L_p$, $0$, for functions whose spectrum is contained in a closed ball or a closed spherical layer. As an application, a discrete description of Lizorkin–Triebel spaces in terms of coordinate differences of positive order is given.
Keywords: $L_p$-inequality, Riesz-type inequality, Bernstein-type inequality, Bohr–Favard type inequality, $L_p$ space, Lizorkin–Triebel space, functions whose spectrum is contained in a closed ball or a closed spherical layer, Young's inequality.
Mots-clés : Fourier transform 
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N. L. Kudryavtsev. $L_p$-Inequalities for Differences and Derivatives of Positive Order for Functions with Spectrum in the Ball or Spherical Layer. Matematičeskie zametki, Tome 95 (2014) no. 3, pp. 433-444. http://geodesic.mathdoc.fr/item/MZM_2014_95_3_a9/

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