hold with some constant C independent of f? (Unless otherwise specified, all integrals are taken with respect to the standard Lebesgue measure on R.) Denoting w := u−1, we can reformulate the above… (More)

In this paper we are proving that Sawyer type condition for boundedness work for the two weight estimates of individual Haar multipliers, as well as for the Haar shift and other “well localized”… (More)

In the paper we consider Calderón-Zygmund operators in nonhomogeneous spaces. We are going to prove the analogs of classical results for homogeneous spaces. Namely, we prove that a Calderón-Zygmund… (More)

1. Preliminaries The goal of this paper is to consider the boundedness of singular integral operators with Calderr on-Zygmund kernels in L 2 (), where is an arbitrary measure without atoms in R n. We… (More)

We introduce a new approach to Nehari’s problem. This approach is based on some kind of fixed point theorem and allows us to obtain some useful generalizations of Nehari’s and Adamyan – Arov – Krein… (More)

Main result of this paper is the following theorem: given δ, 0 < δ < 1/3 and n ∈ N there exists an (n + 1) × n inner matrix function F ∈ H∞ (n+1)×n such that I ≥ F ∗(z)F (z) ≥ δI ∀z ∈ D, but the norm… (More)

The stochastic optimal control uses the differential equation of Bellman and its solution—the Bellman function. We show how the homonym function in harmonic analysis is (and how it is not) the same… (More)

The first author showed in [18] that the Hilbert transform lies in the closed convex hull of dyadic singular operators —so-called dyadic shifts. We show here that the same is true in any Rn —the… (More)