Dyadic representation theorem using smooth wavelets with compact support

Abstract

The representation of a general Calderón--Zygmund operator in terms of dyadic Haar shift operators first appeared as a tool to prove the $A_2$ theorem, and it has found a number of other applications. In this paper we prove a new dyadic representation theorem by using smooth compactly supported wavelets in place of Haar functions. A key advantage of this is that we achieve a faster decay of the expansion when the kernel of the general Calderón--Zygmund operator has additional smoothness.

v2: incorporated referees' comments, to appear in Journal of Fourier Analysis and Applications, 18 pages

References in corpus (3)

• Weighted little bmo and two-weight inequalities for Journé commutators
• A T(P) theorem for Sobolev spaces on domains
• Wavelet Representation of Singular Integral Operators

Cited by in corpus (1)

• Initial $L^2\times \cdots \times L^2$ bounds for multilinear operators