Abstract:

Let (X,d,μ) be a space of homogeneous type and L be a nonnegative self-adjoint operator on L2(X) whose heat kernels satisfy Gaussian upper bounds. In this article, we introduce the weighted variable Besov space associated with the operator L and demonstrate that Peetre maximal functions can be used to characterize this space. Furthermore, we provide a detailed study of its atomic decompositions.

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