Weighted Bourgain-Morrey-Besov type and Triebel-Lizorkin type spaces associated with operators

2025/05/25 by Bai, Tengfei, Guo, Pengfei, Xu, Jingshi
#46E36 #46F05 #47B38 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2505.19135

Abstract

Let (X,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 enjoys a Gaussian upper bound. We introduce the weighted homogeneous Bourgain-Morrey-Besov type spaces and Triebel-Lizorkin type spaces associated with the operator L. We obtain their continuous characterizations in terms of Peetre maximal functions, noncompactly supported functional calculus, heat kernel. Atomic and molecular decompositions of weighted homogeneous Bourgain-Morrey-Besov type spaces and Triebel-Lizorkin type spaces are also given. As an application, we obtain the boundedness of the fractional power of L, the spectral multiplier of L on Bourgain-Morrey-Besov type spaces and Triebel-Lizorkin type spaces.

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