The linear bound in A₂ for Calderón-Zygmund operators: a survey

• Autorzy: Michael Lacey
• Języki publikacji: EN

Abstrakty

EN

For an L²-bounded Calderón-Zygmund Operator T acting on $L²(ℝ^{d})$, and a weight w ∈ A₂, the norm of T on L²(w) is dominated by $C_T ||w||_{A₂}$. The recent theorem completes a line of investigation initiated by Hunt-Muckenhoupt-Wheeden in 1973 (MR0312139), has been established in different levels of generality by a number of authors over the last few years. It has a subtle proof, whose full implications will unfold over the next few years. This sharp estimate requires that the A₂ character of the weight can be exactly once in the proof. Accordingly, a large part of the proof uses two-weight techniques, is based on novel decomposition methods for operators and weights, and yields new insights into the Calderón-Zygmund theory. We survey the proof of this Theorem in this paper.

Kategorie tematyczne

• 42B35: Function spaces arising in harmonic analysis
• 47B38: Operators on function spaces (general)
• 42B20: Singular and oscillatory integrals (Calder\'on-Zygmund, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2011
• Tom: 95
• Numer: 1
• Strony: 97-114

Daty

wydano

2011

Twórcy

autor

Michael Lacey

• School of Mathematics, Georgia Institute of Technology, Atlanta GA 30332, USA

Identyfikatory

DOI

10.4064/bc95-0-7