Variable Triebel-Lizorkin-Lorentz spaces associated to operators. (English) Zbl 1509.46026
Summary: Let \((X, d, \mu)\) be a space of homogenous type and \(L\) be a nonnegative self-adjoint operator on \(L^2(X)\) with heat kernels satisfying Gaussian upper bounds. In this paper, we introduce the variable Triebel-Lizorkin-Lorentz space associated to the operator \(L\) on spaces of homogenous type and prove that this space can be characterized via the Peetre maximal functions. Then we establish an atomic decomposition for this space.
MSC:
| 46E36 | Sobolev (and similar kinds of) spaces of functions on metric spaces; analysis on metric spaces |
| 42B35 | Function spaces arising in harmonic analysis |
| 47B90 | Operator theory and harmonic analysis |
Keywords:
variable exponents; Lorentz spaces; metric measure space; heat kernel; maximal characterization; atomic characterizationsReferences:
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