‐bounded ‐calculus for sectorial operators via generalized Gaussian estimates |
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Authors: | Peer Christian Kunstmann Alexander Ullmann |
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Institution: | 1. +49 2. 721 3. 608 4. 46195+49 5. 46214;6. Department of Mathematics, Karlsruhe Institute of Technology, Karlsruhe, Germany |
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Abstract: | We show that, for negative generators of analytic semigroups, a bounded ‐calculus self‐improves to an ‐bounded ‐calculus in an appropriate scale of ‐spaces if the semigroup satisfies suitable generalized Gaussian estimates. As application of our result we obtain that large classes of differential operators have an ‐bounded ‐calculus. |
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Keywords: | Functional calculus Calderó n‐Zygmund theory elliptic operators 47A60 42B25 47B38 47D06 |
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