On the Interpolation of Analytic Maps
A.M. Savchuk, A.A. Shkalikov

TL;DR
This paper proves that an analytic map between certain Banach space interpolation spaces maintains boundedness properties within intermediate spaces, with explicit bounds derived from endpoint estimates.
Contribution
It establishes interpolation results for analytic maps between Banach spaces, providing explicit bounds for the map's behavior in intermediate spaces.
Findings
Analytic maps preserve boundedness in interpolated Banach spaces.
Explicit bounds relate endpoint estimates to intermediate space behavior.
Results apply to dense, continuous embeddings of Banach spaces.
Abstract
Let (E_0,E_1) and (H_0,H_1) be a pair of Banach spaces with dense and continuous embeddings E_1 into E_0, H_1 into H_0. For denote by the ball of radius R centered at zero in the interpolation spaces E_\theta. Assume that an analytic map maps the ball B_0(0,R) into H_0, maps B_1(0,R) into H_1 and for the estimates hold. Then for all and r<R maps the ball into and the same estimate holds for if the constant is replaced by .
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Taxonomy
TopicsHistorical Geography and Cartography · Satellite Image Processing and Photogrammetry · Constraint Satisfaction and Optimization
