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Anisotropic function spaces and related semi–linear hypoelliptic equations
Author(s) -
Dachkovski Serguei
Publication year - 2003
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.200310002
Subject(s) - mathematics , hypoelliptic operator , smoothness , besov space , pure mathematics , function space , mathematical analysis , truncation (statistics) , fubini's theorem , interpolation space , partial differential equation , functional analysis , biochemistry , chemistry , statistics , gene , linear differential equation
Abstract Looking for the best possible smoothness (in terms of the upper index of the Besov spaces) for the solution of some semi–linear equations we consider a model case of a hypoelliptic operator, which acts between anisotropic Besov spaces. To obtain the best regularity we need some properties for the corresponding spaces, which we prove here. In particular we prove Fatou, Fubini and truncation properties. We give also some characterisations of the Besov and Triebel–Lizorkin spaces.