A limited-range Calderón-Zygmund theorem

Abstract

For a limited range of indices $p$, we obtain $L^p({\mathbb{R}}^n)$ boundedness for singular integral operators whose kernels satisfy a condition weaker than the typical Hörmander smoothness estimate. These operators are assumed to be bounded (or weakly bounded) on $L^s({\mathbb{R}}^n)$ for some index $s$. Our estimates are obtained via interpolation from the appropriate weak-type estimates. We provide two proofs of this result. One proof is based on the Calderón-Zygmund decomposition, while the other uses ideas of Nazarov, Treil, and Volberg.

9 pages

References in corpus (1)

• A different approach to endpoint weak-type estimates for Calderón-Zygmund operators