Proposition 7.14 (Weighted Schauder estimate, the global version) . [056G] Original official author HTML, exact retained edition. Historical TeX conversion verdicts remain unchanged. Cited-edition alignment and mathematical self-containment are not assessed.
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Proposition 7.14 (Weighted Schauder estimate, the global version).
For every α ∈ ( 0 , 1 ) \alpha\in(0,1) C > 0 C>0 | t | ≪ 1 |t|\ll 1 u ∈ 𝔄 u\in\mathfrak{A}
(7.169) ‖ u ‖ C δ , ν , μ 2 , α ( X ^ t ) ≤ C ( ‖ Δ u ‖ C δ , ν + 2 , μ 0 , α ( X ^ t ) + ‖ u ‖ C δ , ν , μ 0 ( X ^ t ) ) . \displaystyle\|u\|_{C_{\delta,\nu,\mu}^{2,\alpha}(\widehat{X}_{t})}\leq C\Big(\|\Delta u\|_{C_{\delta,\nu+2,\mu}^{0,\alpha}(\widehat{X}_{t})}+\|u\|_{C_{\delta,\nu,\mu}^{0}(\widehat{X}_{t})}\Big).