Structured continuous maximal regularity sharpens via weak compactness of convolution operators, delivering new proofs for L1-maximal regularity, Baillon's theorem extensions, and resolution of an abstract input-to-state stability open problem.
Laplace-Carleson embeddings and infinity-norm admissibility
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abstract
A full characterization of the boundedness of Laplace--Carleson embeddings on $L^\infty$ is provided, in terms of the Carleson intensity of the respective measure and of a suitable weighted Berezin transform of the measure. Moreover, boundedness results, and in some cases full characterizations of boundedness, are proved for a large class of Orlicz spaces. These findings are crucial for characterizing admissibility of control operators for linear diagonal semigroup systems in a variety of contexts. A particular focus is laid on essentially bounded inputs.
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2026 1verdicts
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Implications of structured continuous maximal regularity
Structured continuous maximal regularity sharpens via weak compactness of convolution operators, delivering new proofs for L1-maximal regularity, Baillon's theorem extensions, and resolution of an abstract input-to-state stability open problem.