与算子相关的加权齐次Bourgain-Morrey Besov-Triebel-Lizorkin空间的预对偶
Preduals of weighted homogeneous Bourgain-Morrey Besov-Triebel-Lizorkin spaces associated with operators
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中文总结 AI 辅助
研究齐次型空间上与算子相关的加权齐次Bourgain-Morrey Besov-Triebel-Lizorkin空间的预对偶，引入块空间并证明其与单位分解选择无关。
中文摘要 AI 辅助
设$(X,\rho,\mu)$为满足$\mu(X)=\infty$、倍测度性质和逆倍测度条件的齐次型空间。设$L$为$L^2(X)$上的非负自伴算子，其热核具有高斯上界。首先，我们研究$X$上加权Bourgain-Morrey空间的预对偶及其性质，如格性质和完备性。然后我们引入加权齐次Besov-Triebel-Lizorkin块空间。证明了这些块空间是与算子$L$相关的加权齐次Bourgain-Morrey Besov-Triebel-Lizorkin空间的预对偶。因此，这些块空间与单位分解的选择无关。
英文摘要
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.
