Francesco Di Plinio

Domination of multilinear singular integrals by positive sparse forms

We establish a uniform domination of the family of trilinear multiplier forms with singularity over a one-dimensional subspace by positive sparse forms involving

On weighted norm inequalities for the Carleson and Walsh–Carleson operator

L^p

The Euler equations in planar nonsmooth convex domains

-averages. This class includes the adjoint forms to the bilinear Hilbert transforms. Our result strengthens the

Weak-Lp bounds for the Carleson and Walsh–Carleson operators

L^p

Grisvard's Shift Theorem Near

-boundedness proved in \cite{MTT} and entails as a corollary a rich multilinear weighted theory. In particular, we obtain

L^\infty

L^{q_1}(v_1) \times L^{q_2}(v_2)

and Yudovich Theory on Polygonal Domains

-boundedness of the bilinear Hilbert transform when the weights

A modulation invariant Carleson embedding theorem outside local L 2

v_j

Navier–Stokes–Voigt Equations with Memory in 3D Lacking Instantaneous Kinematic Viscosity

belong to the class

Square functions for bi-Lipschitz maps and directional operators

A_{\frac{q+1}{2}}\cap RH_2