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R s ‐bounded H ∞ ‐calculus for sectorial operators via generalized Gaussian estimates
Author(s) -
Kunstmann Peer Christian,
Ullmann Alexander
Publication year - 2015
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201300132
Subject(s) - mathematics , bounded function , time scale calculus , differential calculus , semigroup , calculus (dental) , holomorphic functional calculus , gaussian , pure mathematics , algebra over a field , multivariable calculus , mathematical analysis , finite rank operator , banach space , medicine , physics , dentistry , quantum mechanics , control engineering , engineering
We show that, for negative generators of analytic semigroups, a bounded H ∞ ‐calculus self‐improves to an R s ‐bounded H ∞ ‐calculus in an appropriate scale of L p ‐spaces if the semigroup satisfies suitable generalized Gaussian estimates . As application of our result we obtain that large classes of differential operators have an R s ‐bounded H ∞ ‐calculus.