18 citations · 95 across the 21 of their papers we have counts for
5 papers · 2 filters
Sharp estimates involving and constants, and their applications to PDE
Alexander Reznikov, Oleksandra Beznosova
It is a well known fact that the union of the Reverse Hölder classes coincides with the union of the Muckenhoupt classes , but the constant of the weight , which…
The proof of conjecture in a geometrically doubling metric space
Fedor Nazarov, Alexander Reznikov, Alexander Volberg
We give a proof of the conjecture in geometrically doubling metric spaces (GDMS), i.e. a metric space where one can fit not more than a fixed amount of disjoint balls of radi…
Sharp weak type estimates for weights in the class
Alexander Reznikov
We get sharp estimates for the distribution function of nonnegative weights, which satisfy so called condition. For particular choices of parameters , thi…
A sharp estimate of weighted dyadic shifts of complexity 0 and 1
Alexander Reznikov, Sergei Treil, Alexander Volberg
A simple shortcut to proving sharp weighted estimates for the Martingale Transform and for the dyadic shift of order 1 (and so for the Hilbert transform) is presented. It is a unif…
Random "dyadic" lattice in geometrically doubling metric space and conjecture
Alexander Reznikov, Alexander Volberg
Recently three proofs of the -conjecture were obtained. All of them are "glued" to euclidian space and a special choice of one random dyadic lattice. We build a random "dyadic…