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Preduals of weighted homogeneous Bourgain-Morrey Besov-Triebel-Lizorkin spaces associated with operators

  • Tengfei Bai
  • Pengfei Guo
  • Jingshi Xu
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Abstract

Let (X,ρ,μ) be a space of homogeneous type satisfying μ(X) =∞, the doubling property and the reverse doubling condition. Let L be a nonnegative self-adjoint operator on L2(X) whose heat kernel has a Gaussian upper bound. First, we study the preduals of weighted Bourgain-Morrey spaces on X and their properties, such as lattice property and completeness. Then we introduce the weighted homogeneous Besov-Triebel-Lizorkin block spaces. It is shown that they are the preduals of weighted homogeneous Bourgain-Morrey Besov-Triebel-Lizorkin spaces associated with the operator L. Consequently, these block spaces are independent of the choice of partitions of unity.

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Cite

BibTeXRIS
BibTeX
@misc{bai2026preduals,
  title = {{Preduals of weighted homogeneous Bourgain-Morrey Besov-Triebel-Lizorkin spaces associated with operators}},
  author = {Tengfei Bai and Pengfei Guo and Jingshi Xu},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.29980},
  eprint = {2609.29980},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.29980},
}
RIS
TY  - UNPB
TI  - Preduals of weighted homogeneous Bourgain-Morrey Besov-Triebel-Lizorkin spaces associated with operators
AU  - Tengfei Bai
AU  - Pengfei Guo
AU  - Jingshi Xu
PY  - 2026
DA  - 2026/09/24
PB  - arXiv
DO  - 10.48550/arxiv.2609.29980
UR  - https://arxiv.org/abs/2609.29980
AB  - Let (X,ρ,μ) be a space of homogeneous type satisfying μ(X) =∞, the doubling property and the reverse doubling condition. Let L be a nonnegative self-adjoint operator on L^2(X) whose heat kernel has a Gaussian upper bound. First, we study the preduals of weighted Bourgain-Morrey spaces on X and their properties, such as lattice property and completeness. Then we introduce the weighted homogeneous Besov-Triebel-Lizorkin block spaces. It is shown that they are the preduals of weighted homogeneous Bourgain-Morrey Besov-Triebel-Lizorkin spaces associated with the operator L. Consequently, these block spaces are independent of the choice of partitions of unity.
ER  -