TY - JOUR
T1 - Sharp estimates for conditionally centered moments and for compact operators on LP spaces
AU - Shargorodsky, Eugene
AU - Sharia, Teo
N1 - Publisher Copyright:
© 2022 The Authors. Mathematische Nachrichten published by Wiley-VCH GmbH.
PY - 2023/1
Y1 - 2023/1
N2 - Let (Formula presented.) be a probability space, ξ be a random variable on (Formula presented.), (Formula presented.) be a sub-σ-algebra of (Formula presented.), and let (Formula presented.) be the corresponding conditional expectation operator. We obtain sharp estimates for the moments of (Formula presented.) in terms of the moments of ξ. This allows us to find the optimal constant in the bounded compact approximation property of (Formula presented.), (Formula presented.).
AB - Let (Formula presented.) be a probability space, ξ be a random variable on (Formula presented.), (Formula presented.) be a sub-σ-algebra of (Formula presented.), and let (Formula presented.) be the corresponding conditional expectation operator. We obtain sharp estimates for the moments of (Formula presented.) in terms of the moments of ξ. This allows us to find the optimal constant in the bounded compact approximation property of (Formula presented.), (Formula presented.).
KW - bounded compact approximation property
KW - conditionally centred moments
KW - sharp estimates
UR - http://www.scopus.com/inward/record.url?scp=85144197306&partnerID=8YFLogxK
U2 - 10.1002/mana.202100217
DO - 10.1002/mana.202100217
M3 - Article
AN - SCOPUS:85144197306
SN - 0025-584X
VL - 296
SP - 368
EP - 381
JO - Mathematische Nachrichten
JF - Mathematische Nachrichten
IS - 1
ER -