TY - JOUR
T1 - Interpolation of derivatives and ultradifferentiable regularity
AU - Rainer, Armin
AU - Schindl, Gerhard
N1 - Publisher Copyright:
© 2024 The Author(s). Mathematische Nachrichten published by Wiley-VCH GmbH.
PY - 2025/2
Y1 - 2025/2
N2 - Interpolation inequalities for (Formula presented.) functions allow to bound derivatives of intermediate order (Formula presented.) by bounds for the derivatives of order 0 and (Formula presented.). We review various interpolation inequalities for (Formula presented.) -norms ((Formula presented.)) in arbitrary finite dimensions. They allow us to study ultradifferentiable regularity by lacunary estimates in a comprehensive way, striving for minimal assumptions on the weights.
AB - Interpolation inequalities for (Formula presented.) functions allow to bound derivatives of intermediate order (Formula presented.) by bounds for the derivatives of order 0 and (Formula presented.). We review various interpolation inequalities for (Formula presented.) -norms ((Formula presented.)) in arbitrary finite dimensions. They allow us to study ultradifferentiable regularity by lacunary estimates in a comprehensive way, striving for minimal assumptions on the weights.
KW - Denjoy–Carleman classes
KW - ultradifferentiable regularity
KW - interpolation inequalities
KW - lacunary estimates
UR - https://arxiv.org/pdf/2312.07020.pdf
UR - https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.202300567
UR - http://www.scopus.com/inward/record.url?scp=85212488185&partnerID=8YFLogxK
U2 - 10.1002/mana.202300567
DO - 10.1002/mana.202300567
M3 - Article
SN - 0025-584X
VL - 298
SP - 617
EP - 635
JO - Mathematische Nachrichten
JF - Mathematische Nachrichten
IS - 2
ER -