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Traces of Besov and Lizorkin--Triebel spaces to thick subsets of ℝn
Abstract
Let d∈ [0, n] and let E⊂ ℝn be a closed d-thick set. Given p∈ [1, ∞], q∈ (0, ∞], and s∈ ((n−d)/p, 1), we provide an intrinsic description of the trace-space of the Besov space Bsp, q(ℝn) to E. If, in addition, p<∞, we give an intrinsic description of the trace-space of the Lizorkin--Triebel space Fsp, q(ℝn) to E.
Related
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- On Besov and Triebel-Lizorkin spaces associated with the Grushin operator
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BibTeX
@misc{chikalov2026traces,
title = {{Traces of Besov and Lizorkin--Triebel spaces to thick subsets of $\mathbbR^n$}},
author = {Aleksei Y. Chikalov},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.19520},
eprint = {2609.19520},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.19520},
}
RIS
TY - UNPB
TI - Traces of Besov and Lizorkin--Triebel spaces to thick subsets of ℝ^n
AU - Aleksei Y. Chikalov
PY - 2026
DA - 2026/09/17
PB - arXiv
DO - 10.48550/arxiv.2609.19520
UR - https://arxiv.org/abs/2609.19520
AB - Let d∈ [0, n] and let E⊂ ℝ^n be a closed d-thick set. Given p∈ [1, ∞], q∈ (0, ∞], and s∈ ((n−d)/p, 1), we provide an intrinsic description of the trace-space of the Besov space B^s_p, q(ℝ^n) to E. If, in addition, p<∞, we give an intrinsic description of the trace-space of the Lizorkin--Triebel space F^s_p, q(ℝ^n) to E.
ER -