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Remarks on Complex Interpolation of Some Nonlinear Operators (I)

✍ Scribed by Michael Böhm

Publisher
John Wiley and Sons
Year
1991
Tongue
English
Weight
667 KB
Volume
153
Category
Article
ISSN
0025-584X

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✦ Synopsis

Bo n B , be an operator satisfying some conditions such as continuity, estimates etc. in terms of the norms of A j , Bj ( j = 0, 1). We consider the question which one of these properties is inherited to T when A , n A, and E , n B, are equipped with the norm of A, and B,. 0. * Furthermore, let D, := {f: S + AA: 3m > 0, n E R, a E AA s.t. f(z) = emz2+nra} , D , := linear hull of D,, r : S + unit disc in Cconformal mapping with r(0) = 0. Note: D, := {f : f + AA: 3p > 0, g E D2 s.t. f(z) = er(r-e)2a + z(z) g(z)} , Ir(it)l = Ir(1 + it)l = 1 for all real t , and for a E AA let D:= u D,.

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