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Composition semigroups on the minimal Möbius invariant space. (English) Zbl 1438.20050

Summary: The sufficient condition for the \((\varphi_t)_{t \ge 0}\) belong to \(B_1\) is provided and then the composition semigroups are bounded on \(B_1\). The domain of infinitesimal generator under strong continuity is discussed. The composition semigroups are proved to be not continuous in the uniform topology. In addition, the necessary and sufficient condition under which composition semigroups are strongly continuous on \(B_p\) (\(1 < p < \infty\)) is described.

MSC:

20M05 Free semigroups, generators and relations, word problems
20M99 Semigroups
32A37 Other spaces of holomorphic functions of several complex variables (e.g., bounded mean oscillation (BMOA), vanishing mean oscillation (VMOA))
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