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math.CA2016
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)\,…
math.CA2016★ 2 cited
Remez-type inequalities for the hyperbolic cross polynomials
V. Temlyakov, S. Tikhonov
In this paper we study the Remez-type inequalities for trigonometric polynomials with harmonics from hyperbolic crosses. The interrelation between the Remez and Nikolskii inequalit…
math.FA2016★ 4 cited
Jacobi weights, fractional integration, and sharp Ulyanov inequalities
Polina Glazyrina, Sergey Tikhonov
We consider functions L_p-integrable with Jacobi weights on [-1,1] and prove Hardy--Littlewood type inequalities for fractional integrals. As applications, we obtain the sharp (L_p…