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ArticleOriginal scientific text

Title

Nonclassical interpolation in spaces of smooth functions

Authors 1

Affiliations

  1. Mathematical Department, Voronezh State University, Universitetskaia pl. 1, 394693, Voronezh, Russia

Abstract

We prove that the fractional BMO space on a one-dimensional manifold is an interpolation space between C and C1. We also prove that BMO1 is an interpolation space between C and C2. The proof is based on some nonclassical interpolation constructions. The results obtained cannot be transferred to spaces of functions defined on manifolds of higher dimension. The interpolation description of fractional BMO spaces is used at the end of the paper for the proof of the boundedness of commutators of the Hilbert transform.

Bibliography

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Studia Mathematica
1999/135/3
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Pages:
203-218
Main language of publication
English
Received
1998-03-02
Accepted
1999-01-18
Published
1999
Exact and natural sciences