TY - JOUR
T1 - Complex interpolation of R-norms, duality and foliations
AU - Berndtsson, Bo
AU - Cordero-Erausquin, Dario
AU - Klartag, Bo’az
AU - Rubinstein, Yanir A.
N1 - Publisher Copyright:
© European Mathematical Society 2020.
PY - 2020
Y1 - 2020
N2 - The complex method of interpolation, going back to Calderón and Coifman et al., on the one hand, and the Alexander–Wermer–Słodkowski theorem on polynomial hulls with convex fibers, on the other hand, are generalized to a method of interpolation of real (finite-dimensional) Banach spaces and of convex functions. The underlying duality in this method is given by the Legendre transform. Our results can also be interpreted as new properties of solutions of the homogeneous complex Monge–Ampère equation.
AB - The complex method of interpolation, going back to Calderón and Coifman et al., on the one hand, and the Alexander–Wermer–Słodkowski theorem on polynomial hulls with convex fibers, on the other hand, are generalized to a method of interpolation of real (finite-dimensional) Banach spaces and of convex functions. The underlying duality in this method is given by the Legendre transform. Our results can also be interpreted as new properties of solutions of the homogeneous complex Monge–Ampère equation.
KW - Complex interpolation
KW - Convex geometry
UR - http://www.scopus.com/inward/record.url?scp=85084816387&partnerID=8YFLogxK
U2 - 10.4171/JEMS/927
DO - 10.4171/JEMS/927
M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???
AN - SCOPUS:85084816387
SN - 1435-9855
VL - 22
SP - 477
EP - 505
JO - Journal of the European Mathematical Society
JF - Journal of the European Mathematical Society
IS - 2
ER -