8 citations
- Universitat Autònoma de BarcelonaES4 papers
- Institució Catalana de Recerca i Estudis AvançatsES3 papers
- University of AlbertaCA3 papers
- Centre de Recerca MatemàticaES2 papers
- N.N. Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of SciencesRU1 paper
- Ural Branch of the Russian Academy of SciencesRU1 paper
5 papers · 1 filter
Estimates of the asymptotic Nikolskii constants for spherical polynomials
Feng Dai, Dmitry Gorbachev, Sergey Tikhonov
Let denote the space of spherical polynomials of degree at most on the unit sphere that is equipped with the surface Lebesgue mea…
Nikolskii inequality for lacunary spherical polynomials
Feng Dai, Dmitry Gorbachev, Sergey Tikhonov
We prove that for , the asymptotic order of the usual Nikolskii inequality on (also known as the reverse Hölder's inequality) can be significantly improved i…
Nikolskii constants for polynomials on the unit sphere
Feng Dai, Dmitry Gorbachev, Sergey Tikhonov
This paper studies the asymptotic behavior of the exact constants of the Nikolskii inequalities for the space of spherical polynomials of degree at most on the unit sph…
Riesz potential and maximal function for Dunkl transform
D. V. Gorbachev, V. I. Ivanov, S. Yu. Tikhonov
We study weighted -boundedness properties of Riesz potentials and fractional maximal functions for the Dunkl transform. In particular, we obtain the weighted Hardy-Litt…
Doubling condition at the origin for non-negative positive definite functions
Dmitry Gorbachev, Sergey Tikhonov
We study upper and lower estimates as well as the asymptotic behavior of the sharp constant in the doubling-type condition at the origin \[ \frac{1}{|V|}\int_{V}f(x)\,…