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Real-analytic operator-valued functions defined in BMO. (English) Zbl 0709.47012

Analysis and partial differential equations, Coll. Pap. dedic. Mischa Cotlar, Lect. Notes Pure Appl. Math. 122, 85-100 (1990).
[For the entire collection see Zbl 0684.00014.]
Following ideas of C. Kenig and Y. Meyer [North-Holland Math. Stud. III, 123-143 (1985; Zbl 0641.47039)], the authors investigate analyticity properties of various operators of the form \((e^{2\alpha}De^{2\beta}D)^{1/2}(e^{\alpha +\beta}D)^{-1}\), regarded as functions of the bounded mean oscillation functions \(\alpha\),\(\beta: {\mathbb{R}}\to {\mathbb{R}}\), where iD denotes differentiation \((i^ 2=-1)\).
Reviewer: A.L.Andrew

MSC:

47A56 Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones)
32A37 Other spaces of holomorphic functions of several complex variables (e.g., bounded mean oscillation (BMOA), vanishing mean oscillation (VMOA))
46E15 Banach spaces of continuous, differentiable or analytic functions
47E05 General theory of ordinary differential operators