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Remarks on Complex Interpolation of Some Nonlinear Operators (I)
Author(s) -
Böhm Michael
Publication year - 1991
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.19911530118
Subject(s) - mathematics , interpolation (computer graphics) , norm (philosophy) , nonlinear system , operator (biology) , pure mathematics , linear interpolation , algebra over a field , combinatorics , discrete mathematics , mathematical analysis , telecommunications , computer science , biochemistry , chemistry , physics , repressor , quantum mechanics , political science , transcription factor , law , gene , frame (networking) , polynomial
Let A j , B j be complex B ‐spaces, j = 0, 1, A θ and B θ –the complex‐interpolation spaces generated by the couples ( A 0 , A 1 ) and ( B 0 , B 1 ), resp., by CALDERON'S/LIONS'S method. Let T: A 0 ∧ A 1 → B 0 → B 1 be an operator satisfying some conditions such as continuity, estimates etc. in terms of the norms of A j , B j ( j = 0, 1). We consider the question which one of these properties is inherited to T when A 0 → A 1 and B 0 → B 1 are equipped with the norm of A θ and B θ .