Preduals of weighted homogeneous Bourgain-Morrey Besov-Triebel-Lizorkin spaces associated with operators
Year: 2026
Type: preprint
Abstract: Let $(X,ρ,μ)$ be a space of homogeneous type satisfying $μ(X) =\infty$, 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.
Source: arXiv (Cornell University)
Authors: Bai, Tengfei, Guo, Pengfei, Xu, Jingshi
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G1946780875
OpenAlex ID: W7214329460