Geodesic
Nikolskii--Bernstein constants in $L^{p}$ on~the~sphere with~Dunkl~weight
Čebyševskij sbornik, Tome 21 (2020) no. 4, pp. 302-307

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We study the sharp Nikol'skii–Bernstein constants for spherical polynomials in the space $L^{p}(\mathbb{S}^{d})$ with the Dunkl weight. An interrelationship with one-dimensional constants for algebraic polynomials in the space $L^{p}[-1,1]$ with the Gegenbauer weight is established.
Keywords: Euclidean sphere, Dunkl weight, Gegenbauer weight, spherical polynomials, Nikolskii constant, Bernstein inequality. 
@article{CHEB_2020_21_4_a23,
     author = {D. V. Gorbachev and N. N. Dobrovol'skii},
     title = {Nikolskii--Bernstein constants in $L^{p}$ on~the~sphere {with~Dunkl~weight}},
     journal = {\v{C}eby\v{s}evskij sbornik},
     pages = {302--307},
     publisher = {mathdoc},
     volume = {21},
     number = {4},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHEB_2020_21_4_a23/}
}
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D. V. Gorbachev; N. N. Dobrovol'skii. Nikolskii--Bernstein constants in $L^{p}$ on~the~sphere with~Dunkl~weight. Čebyševskij sbornik, Tome 21 (2020) no. 4, pp. 302-307. http://geodesic.mathdoc.fr/item/CHEB_2020_21_4_a23/