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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     author = {N. L. Kudryavtsev},
     title = {$L_p${-Inequalities} for {Differences} and {Derivatives} of {Positive} {Order} for {Functions} with {Spectrum} in the {Ball} or {Spherical} {Layer}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {433--444},
     publisher = {mathdoc},
     volume = {95},
     number = {3},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2014_95_3_a9/}
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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/