Nonclassical interpolation in spaces of smooth functions

• Autorzy: Vladimir I. Ovchinnikov
• Języki publikacji: EN

Abstrakty

EN

We prove that the fractional BMO space on a one-dimensional manifold is an interpolation space between C and $C^1$. We also prove that $BMO^1$ is an interpolation space between C and $C^2$. 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.

Kategorie tematyczne

• 46M35: Abstract interpolation of topological vector spaces
• 46E35: Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1999
• Tom: 135
• Numer: 3
• Strony: 203-218

Daty

wydano

1999

otrzymano

1998-03-02

poprawiono

1999-01-18

Twórcy

autor

Vladimir I. Ovchinnikov

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

Bibliografia

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