Real Analysis Exchange

Sobolev Subspaces of Nowhere Bounded Functions

Pier Domenico Lamberti and Giorgio Stefani

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Abstract

We prove that in any Sobolev space which is subcritical with respect to the Sobolev Embedding Theorem there exists a closed infinite dimensional linear subspace whose non zero elements are nowhere bounded functions. We also prove the existence of a closed infinite dimensional linear subspace whose non zero elements are nowhere $L^q$ functions for suitable values of $q$ larger than the Sobolev exponent.

Article information

Source
Real Anal. Exchange, Volume 41, Number 2 (2016), 367-376.

Dates
First available in Project Euclid: 30 March 2017

Permanent link to this document
https://projecteuclid.org/euclid.rae/1490839338

Mathematical Reviews number (MathSciNet)
MR3597326

Zentralblatt MATH identifier
06848936

Subjects
Primary: 46E35: Sobolev spaces and other spaces of "smooth" functions, embedding theorems, trace theorems
Secondary: 26B05: Continuity and differentiation questions 26B40: Representation and superposition of functions

Keywords
nowhere bounded functions Sobolev spaces Sobolev Embedding

Citation

Lamberti, Pier Domenico; Stefani, Giorgio. Sobolev Subspaces of Nowhere Bounded Functions. Real Anal. Exchange 41 (2016), no. 2, 367--376. https://projecteuclid.org/euclid.rae/1490839338


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