Displaying similar documents to “Interpolation in L p with boundary conditions”

Nonclassical interpolation in spaces of smooth functions

Vladimir Ovchinnikov (1999)

Studia Mathematica

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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 B M O 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...

On the ℒ -characteristic of fractional powers of linear operators

Jürgen Appell, Marilda A. Simões, Petr P. Zabrejko (1994)

Commentationes Mathematicae Universitatis Carolinae

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We describe the geometric structure of the ℒ -characteristic of fractional powers of bounded or compact linear operators over domains with arbitrary measure. The description builds essentially on the Riesz-Thorin and Marcinkiewicz-Stein-Weiss- Ovchinnikov interpolation theorems, as well as on the Krasnosel’skij-Krejn factorization theorem.