Fedor Nazarov

Global well-posedness for the critical 2D dissipative quasi-geostrophic equation

We give an elementary proof of the global well-posedness for the critical 2D dissipative quasi-geostrophic equation. The argument is based on a non-local maximum principle involving appropriate moduli of continuity.

The Tb-theorem on non-homogeneous spaces

0 Introduction: main objects and results 3 0.1 Main results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 0.2 An application of T1-heorem: electric intensity capacity . . . . . . . . . . . . 7 0.3 How to interpret Calderon–Zygmund operator T? . . . . . . . . . . . . . . . 9 0.3.1 Bilinear form is defined on Lipschitz functions . . . . . . . . . . . . . 10 0.3.2 Bilinear form is defined for smooth functions . . . . . . . . . . . . . . 11 0.3.3 Apriori boundedness . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 0.4 Plan of the paper . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

The bellman functions and two-weight inequalities for Haar multipliers

We give necessary and sufficient conditions for two weight norm inequalities for Haar multipliers operators and for square functions. We also give sufficient conditions for two weight norm inequalities for the Hilbert transform.

On the number of nodal domains of random spherical harmonics

Let

Accretive system Tb-theorems on nonhomogeneous spaces

N(f)

Perfect matchings as IID factors on non-amenable groups

be a number of nodal domains of a random Gaussian spherical harmonic

The Bellman function, the two-weight Hilbert transform, and embeddings of the model spacesKθ

f

Bellman function in stochastic control and harmonic analysis

of degree

A remark on the Mahler conjecture: Local minimality of the unit cube

n

Heating of the Ahlfors–Beurling operator, and estimates of its norm

. We prove that as