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Functional Calculus on BMO and Related Spaces

✍ Scribed by G. Bourdaud; M. Lanza de Cristoforis; W. Sickel

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
181 KB
Volume
189
Category
Article
ISSN
0022-1236

No coin nor oath required. For personal study only.

✦ Synopsis

Let f be a Borel measurable function of the complex plane to itself. We consider the nonlinear operator T f defined by T f [g]=f p g, when g belongs to a certain subspace X of the space BMO(R n ) of functions with bounded mean oscillation on the Euclidean space. In particular, we investigate the case in which X is the whole of BMO, the case in which X is the space VMO of functions with vanishing mean oscillation, and the case in which X is the closure in BMO of the smooth functions with compact support. We characterize those f's for which T f maps X to itself, those f's for which T f is continuous from X to itself, and those f's for which T f is differentiable in X.

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