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Matrix-weighted Z-spaces and tent spaces:characterizations, duality and interpolation
Abstract
Let α∈ℝ, 0<p<∞, 0<q,r≤∞, and W be a matrix 𝒜p weight on ℝn. We introduce the matrix-weighted Z-spaces Zp,q,rα(W) and tent spaces Tp,q,rα(W) on the upper half-space and establish their characterizations using reducing operators. We then characterize homogeneous matrix-weighted Besov and Triebel--Lizorkin spaces in terms of the corresponding Z-spaces and tent spaces, respectively, using Schwartz kernels satisfying Tauberian and finite moment conditions. Furthermore, we establish duality for the matrix-weighted Z-spaces and tent spaces and obtain real and complex interpolation results for these spaces and the associated homogeneous matrix-weighted Besov and Triebel--Lizorkin spaces.
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BibTeX
@misc{bai2026matrixweighted,
title = {{Matrix-weighted $Z$-spaces and tent spaces:characterizations, duality and interpolation}},
author = {Tengfei Bai and Pengfei Guo and Jingshi Xu},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.04810},
eprint = {2611.04810},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.04810},
}
RIS
TY - UNPB
TI - Matrix-weighted Z-spaces and tent spaces:characterizations, duality and interpolation
AU - Tengfei Bai
AU - Pengfei Guo
AU - Jingshi Xu
PY - 2026
DA - 2026/11/03
PB - arXiv
DO - 10.48550/arxiv.2611.04810
UR - https://arxiv.org/abs/2611.04810
AB - Let α∈ℝ, 0<p<∞, 0<q,r≤∞, and W be a matrix 𝒜_p weight on ℝ^n. We introduce the matrix-weighted Z-spaces Z^p,q,r_α(W) and tent spaces T^p,q,r_α(W) on the upper half-space and establish their characterizations using reducing operators. We then characterize homogeneous matrix-weighted Besov and Triebel--Lizorkin spaces in terms of the corresponding Z-spaces and tent spaces, respectively, using Schwartz kernels satisfying Tauberian and finite moment conditions. Furthermore, we establish duality for the matrix-weighted Z-spaces and tent spaces and obtain real and complex interpolation results for these spaces and the associated homogeneous matrix-weighted Besov and Triebel--Lizorkin spaces.
ER -