An interpolation theorem for sublinear operators on non-homogeneous metric measure spaces
Copyright policy )An interpolation theorem for sublinear operators on non-homogeneous metric measure spaces
Let $({\mathcal X}, d, ��)$ be a metric measure space and satisfy the so-called upper doubling condition and the geometrically doubling condition. In this paper, the authors establish an interpolation result that a sublinear operator which is bounded from the Hardy space $H^1(��)$ to $L^{1,\,\infty}(��)$ and from $L^\infty(��)$ to the BMO-type space ${\mathop\mathrm{RBMO}}(��)$ is also bounded on $L^p(��)$ for all $p\in(1,\,\infty)$. This extension is not completely straightforward and improves the existing result.
12pages, 0figure
- Xiamen University China (People's Republic of)
- China Agricultural University China (People's Republic of)
Maximal functions, Littlewood-Paley theory, Hardy space, upper doubling, geometrically doubling, interpolation, metric measure space, Mathematics - Analysis of PDEs, regularized BMO, sublinear operator, RBMO($\mu$)$, Linear operators on function spaces (general), geometric doubling, FOS: Mathematics, sublinear, 42B25, Function spaces arising in harmonic analysis, non-homogeneous space, 47B38, Analysis of PDEs (math.AP), 42B35
Maximal functions, Littlewood-Paley theory, Hardy space, upper doubling, geometrically doubling, interpolation, metric measure space, Mathematics - Analysis of PDEs, regularized BMO, sublinear operator, RBMO($\mu$)$, Linear operators on function spaces (general), geometric doubling, FOS: Mathematics, sublinear, 42B25, Function spaces arising in harmonic analysis, non-homogeneous space, 47B38, Analysis of PDEs (math.AP), 42B35
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