Notes on limits of sobolev spaces and the continuity of interpolation scales

By Mario Milman. 2005

61 citations recorded by the source corpus.

We extend lemmas by Bourgain-Brezis-Mironescu (2001), and Maz'ya-Shaposhnikova (2002), on limits of Sobolev spaces, to the setting of interpolation scales. This is achieved by means of establishing the continuity of real and complex interpolation scales at the end points. A connection to extrapolation theory is developed, and a new application to limits of Sobolev scales is obtained. We also give a new approach to the problem of how to recognize constant functions via Sobolev conditions.

Subfields: Applied Mathematics, Computational Mechanics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/41863b86602735cd88ec25f102a7dd8a2248d4f7

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In Applied Mathematics

1. Xiaolei Xiong
2. Quanhua Xu
3. Zhi Yin
4. Narcisse Randrianantoanina
5. Marius Junge
6. Joel A. Tropp

In Computational Mechanics

1. Xiaolei Xiong
2. Quanhua Xu
3. Zhi Yin

In Numerical Analysis

1. Xiaolei Xiong
2. Quanhua Xu
3. Zhi Yin

Citations in the corpus

• Sobolev, Besov and Triebel-Lizorkin spaces on quantum tori (2015, methodology): “1 q x 1 (X 0,X 1)η,q = q−qkxkX 0 . Here the norm of (X0,X1)η,qis that defined by the K-functional. Then Theorem 3.20 follows from Theorem 5.16 and the first limit above. This is the approach adopted in [38, 47]. It also allows us to determine the other extreme case α= 0 in Theorem 3.20, which was done”