This book is a result of our ten-year fruitful collaboration. It deals with integral operators of
harmonic analysis and their various applications in new, non-standard function spaces …

Given a general dyadic grid D and a sparse family of cubes S= Q jk∈ D, define a dyadic
positive operator AD, S by A_ D, S f (x)= ∑ j, k f_ Q_j^ k χ _ Q_j^ k (x). Given a Banach …

We prove a (sharp) pointwise estimate for positive dyadic shifts of complexity m which is
linear in the complexity. This can be used to give a pointwise estimate for Calderón …

Supplying the missing necessary conditions, we complete the characterisation of the L p→ L
q boundedness of commutators [b, T] of pointwise multiplication and Calderón–Zygmund …

The author gives a mini-survey of several approaches to the A2 theorem, biased towards the
“corona” rather than the “Bellman” side of the coin. There are two new results (a streamlined …

In this paper we provide weighted estimates for rough operators, including rough
homogeneous singular integrals T_ Ω T Ω with Ω ∈ L^ ∞ (S^ n-1) Ω∈ L∞(S n-1) and the …

The two‐weight inequality for the Hilbert transform is characterized for an arbitrary pair of
positive Radon measures σ and w on R. In particular, the possibility of common point …

Let T be an arbitrary L2-bounded Calderón-Zygmund operator, and T♮ its maximal
truncated version. This, then, satisfies the following bound for all p∈(1,∞) and all w∈ Ap …

We provide a counterexample to the Sarason Conjecture for the Bergman space and
present a characterisation of bounded Toeplitz products on the Bergman space in terms of …

We introduce families of weighted grand Lebesgue spaces which generalize weighted
grand Lebesgue spaces (known also as Iwaniec-Sbordone spaces). The generalization …