arXiv subjects
Publications and source records attributed to Cody B. Stockdale.
Two proofs of a weighted weak-type $\left(1,\ldots,1;\frac{1}{m}\right)$ estimate for multilinear Calderón-Zygmund operators are given. The ideas are motivated by different proofs of the classical weak-type $(1,1)$ estimate for Calderón-Zygmund operators. One proof uses the Calderón-Zygmund decomposition, and the other proof is motivated by ideas of Nazarov, Treil, and Volberg.
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.
The purpose of this article is to provide an alternative proof of the weak-type $\left(1,\ldots,1;\frac{1}{m}\right)$ estimate for $m$-multilinear Calderón-Zygmund operators on $\mathbb{R}^n$ first proved by Grafakos and Torres. Subsequent proofs in the bilinear setting have been given by Maldonado and Naibo and also by Pérez and Torres. The proof given here is motivated by the proof of the weak-type $(1,1)$ estimate for Calderón-Zygmund operators in the nonhomogeneous setting by Nazarov, Treil, and Volberg.