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2016 Sobolev Subspaces of Nowhere Bounded Functions
Pier Domenico Lamberti, Giorgio Stefani
Real Anal. Exchange 41(2): 367-376 (2016).

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.

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Pier Domenico Lamberti. Giorgio Stefani. "Sobolev Subspaces of Nowhere Bounded Functions." Real Anal. Exchange 41 (2) 367 - 376, 2016.

Information

Published: 2016
First available in Project Euclid: 30 March 2017

zbMATH: 06848936
MathSciNet: MR3597326

Subjects:
Primary: 46E35
Secondary: 26B05 , 26B40

Keywords: nowhere bounded functions , Sobolev embedding , Sobolev Spaces

Rights: Copyright © 2016 Michigan State University Press

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Vol.41 • No. 2 • 2016
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