Illinois Journal of Mathematics

Peano cubes with derivatives in a Lorentz space

K. Wildrick and T. Zürcher

Full-text: Open access

Abstract

We show that for any length-compact metric space $Y$ and any $1 \lt q\leq n$, there is a continuous surjection in a suitably defined Sobolev–Lorentz space space $W^{1,n,q}([0,1]^n, Y)$. On the other hand, we show that mappings in the space $W^{1,n,1}([0,1]^n, Y)$ satisfy condition (N). This implies that the target $Y$ can be at most $n$-dimensional.

Article information

Source
Illinois J. Math., Volume 53, Number 2 (2009), 365-378.

Dates
First available in Project Euclid: 23 February 2010

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1266934782

Digital Object Identifier
doi:10.1215/ijm/1266934782

Mathematical Reviews number (MathSciNet)
MR2594633

Zentralblatt MATH identifier
1223.46038

Subjects
Primary: 26B35: Special properties of functions of several variables, Hölder conditions, etc.

Citation

Wildrick, K.; Zürcher, T. Peano cubes with derivatives in a Lorentz space. Illinois J. Math. 53 (2009), no. 2, 365--378. doi:10.1215/ijm/1266934782. https://projecteuclid.org/euclid.ijm/1266934782


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