Vector‐valued singular integral operators with rough kernels

Xudong Lai

Mathematische Nachrichten, 2023, vol. 296, issue 6, 2417-2439

Abstract: In this paper, we establish a weak‐type (1,1) boundedness criterion for vector‐valued singular integral operators with rough kernels. As applications, we obtain weak‐type (1,1) bounds for the convolution singular integral operator taking value in the Banach space Y with a rough kernel, the maximal operator taking vector value in Y with a rough kernel and several square functions with rough kernels. Here, Y=[H,X]θ$Y=[H,X]_\theta$ is a complex interpolation space between a Hilbert space H and a UMD space X.

Date: 2023
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https://doi.org/10.1002/mana.202000534

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