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Dirichlet-finite analytic and harmonic functions are BMO

Author: J. L. Schiff
Journal: Proc. Amer. Math. Soc. 108 (1990), 569-570
MSC: Primary 30D55
MathSciNet review: 994786
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Abstract: Based on a result of F. John, an elementary proof is given of the fact that Dirichlet-finite analytic and Dirichlet-finite harmonic functions are of bounded mean oscillation in the unit disk.

References [Enhancements On Off] (What's this?)

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  • [2] F. John, Functions whose gradients are bounded by the reciprocal distance from the boundary of their domain, Russian Math. Surveys 29 (1974), 170-175. MR 0404540 (53:8340)
  • [3] F. John and L. Nirenberg, On functions of bounded mean oscillation, Comm. Pure Appl. Math. 14 (1961), 415-426. MR 0131498 (24:A1348)
  • [4] Y. Kusunoki and M. Taniguchi, Remarks on functions of bounded mean oscillation on Riemann surfaces, Kodai Math. J. 6 (1983), 434-442. MR 717331 (85a:30069)
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