Singular integral operators with operator-valued kernels, and extrapolation of maximal regularity into rearrangement invariant Banach function spaces

We prove two extrapolation results for singular integral operators with operator-valued kernels, and we apply these results in order to obtain the following extrapolation of L p -maximal regularity: if an autonomous Cauchy problem on a Banach space has L p -maximal regularity for some p ∈ ( 1 , ∞ )...

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Bibliographic Details
Published in:Journal of evolution equations 2014-12, Vol.14 (4-5), p.795-828
Main Authors: Chill, Ralph, Fiorenza, Alberto
Format: Article
Language:English
Subjects:
Analysis
Classical Analysis and ODEs
Functional Analysis
Mathematics
Mathematics and Statistics
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Summary:We prove two extrapolation results for singular integral operators with operator-valued kernels, and we apply these results in order to obtain the following extrapolation of L p -maximal regularity: if an autonomous Cauchy problem on a Banach space has L p -maximal regularity for some p ∈ ( 1 , ∞ ) , then it has E w -maximal regularity for every rearrangement invariant Banach function space E with Boyd indices 1 < p E ≤ q E < ∞ and every Muckenhoupt weight w ∈ A p E . We prove a similar result for nonautonomous Cauchy problems on the line.
ISSN:1424-3199
1424-3202
DOI:10.1007/s00028-014-0239-1