Canonical Sobolev Projections of Weak Type (1,1)

by Berkson, Earl; Borgain, Jean; Pelcznski, Aleksander; Wojciechowski, Michal

• ISBN13: 9780821826652
• ISBN10: 0821826654
• Format: Paperback
• Copyright: 2001-03-01
• Publisher: Amer Mathematical Society

Summary

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

Table of Contents

Abstract	viii
Introduction and Notation	1	(4)
Some Properties of Weak Type Multipliers and Canonical Projections of Weak Type (1, 1)	5	(15)
A Class of Weak Type (1, 1) Rational Multipliers	20	(16)
A Subclass of L∞ (R2) \ M1(w) (R2) Induced by L∞ (R)	36	(11)
Some Combinatorial Tools	47	(5)
Necessity Proof for the Second Order Homogeneous Case: A Converse to Corollary (2.14)	52	(4)
Canonical Projections of Weak Type (1, 1) in the Tn Model: Second Order Homogeneous Case	56	(3)
The Non-Homogeneous Case	59	(4)
Reducible Smoothnesses of Order 2	63	(4)
The Canonical Projection of Every Two-Dimensional Smoothness Is of Weak Type (1, 1)	67	(7)
References	74