Canonical Sobolev Projections of Weak Type (1,1)

Introduction and notation Some properties of weak type multipliers and canonical projections of weak type $(1,1)$ A class of weak type $(1,1)$ rational multipliers A subclass of $L^\infty(\mathbb{R}^2)\backslash M_1^{(w)}(\mathbb{R}^2)$ induced by $L^\infty(\mathbb{R})$ Some combinatorial tools Necessity proof for the second order homogeneous case: A converse to Corollary (2.14) Canonical projections of weak type $(1,1)$ in the $\mathbb{T}^n$ model: Second order homogeneous case The non-homogeneous case Reducible smoothnesses of order $2$ the canonical projection of every two-dimensional smoothness is of weak type $(1,1)$ References