Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6414999 | Journal of Functional Analysis | 2016 | 36 Pages |
Abstract
We investigate the boundedness of the Hâ-calculus by estimating the bound b(ε) of the mapping HââB(X): fâ¦f(A)T(ε) for ε near zero. Here, âA generates the analytic semigroup T and Hâ is the space of bounded analytic functions on a domain strictly containing the spectrum of A. We show that b(ε)=O(|logâ¡Îµ|) in general, whereas b(ε)=O(1) for bounded calculi. This generalizes a result by Vitse and complements work by Haase and Rozendaal for non-analytic semigroups. We discuss the sharpness of our bounds and show that single square function estimates yield b(ε)=O(|logâ¡Îµ|).
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Felix L. Schwenninger,