Muckenhoupt–Wheeden theorem for generalized f-Riesz-type potentials

We obtain the Muckenhoupt-Wheeden theorem for some class of potentials. As a consequence, we describe the equivalent norm in the generalized Bessel potential space of negative order.Одержано теорему Макенхаупта–Відена для одного класу потенціалів. Як наслідок, описано еквівалентну норму в просторі узагальнених потенціалів Весселя від'ємного порядку

Exact asymptotic for distribution densities of Levy functionals

A version of the saddle point method is developed, which allows one to describe exactly the asymptotic behavior of distribution densities of Levy driven stochastic integrals with deterministic kernels. Exact asymptotic behavior is established for (a) the transition probability density of a real-valued Levy process; (b) the transition probability density and the invariant distribution density of a Levy driven Ornstein-Uhlenbeck process; (c) the distribution density of the fractional Levy motion.Comment: Revised versio