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• # Artykuł - szczegóły

## Banach Center Publications

2011 | 95 | 1 | 97-114

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

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.

97-114

wydano
2011

### Twórcy

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