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We establish a theory of Besov spaces associated with a family of quasi-metric balls under only the doubling condition on the measure. We introduce the corresponding Hölder spaces as well, and show that the duals of some Besov spaces defined here are equivalent to the corresponding Hölder spaces. As an application, we show that Monge–Ampère singular integral operators are bounded on these spaces.
- Besov spaces
- Hölder spaces
- Monge–Ampère singular integral operators
FingerprintDive into the research topics of 'Besov and Hölder spaces on spaces of homogeneous type'. Together they form a unique fingerprint.
- 2 Finished
1/08/19 → 31/07/20
1/08/19 → 31/07/21