On the L p-boundedness of Calderón-Zygmund operators

Abstract

The main result in this paper is that, for singular integral operators associated with standard kernels, local L 1-estimates imply global L p-estimates for every p ∈ (1, ∞). When combined with the result of Melnikov-Verdera, this yields a complete and self-contained proof of the L p-boundedness of the Cauchy operator on Lipschitz curves and chord-arc curves in the plane.

Keywords

• calderón-zygmund theory
• cauchy operator
• ahlfors regular set
• lipschitz curves
• hardy space
• bmo
• primary
• 42b20
• 42b30
• 42b35
• 46e30
• secondary
• 46b70
• 47b90