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- W2912942526 abstract "Let $$(M, rho , mu )$$ be a metric measure space satisfying the doubling, reverse doubling and noncollapsing conditions, and let $$mathscr {L}$$ be a nonnegative self-adjoint operator acting on $$L^2 (M, dmu )$$ whose heat kernel satisfies the small-time Gaussian upper bound, Hölder continuity and Markov property. In this paper, we establish new characterizations of the “classical” and “nonclassical” Besov and Triebel-Lizorkin spaces associated to $$mathscr {L}$$ introduced by Kerkyacharian and Petrushev. More precisely, we obtain characterizations of these spaces in terms of continuous Littlewood-Paley and Lusin functions associated to the heat semigroup generated by $$mathscr {L}$$ , for complete range of indices. This extends related known results in the classical Euclidean setting to our general setting, and extends corresponding results in (Trans Am Math Soc, 367:121–189, 2015) to complete range of indices." @default.
- W2912942526 created "2019-02-21" @default.
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- W2912942526 date "2022-01-13" @default.
- W2912942526 modified "2023-10-17" @default.
- W2912942526 title "Continuous characterizations of inhomogeneous Besov and Triebel-Lizorkin spaces associated to non-negative self-adjoint operators" @default.
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- W2912942526 doi "https://doi.org/10.1007/s00229-021-01357-9" @default.
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