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- Title
Vector‐valued singular integral operators with rough kernels.
- Authors
Lai, Xudong
- 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.
- Subjects
SINGULAR integrals; INTERPOLATION spaces; INTEGRAL operators; HILBERT space; MAXIMAL functions; BANACH spaces; KERNEL functions
- Publication
Mathematische Nachrichten, 2023, Vol 296, Issue 6, p2417
- ISSN
0025-584X
- Publication type
Article
- DOI
10.1002/mana.202000534