Construction of function spaces close to $L^\infty$ with associate space close to $L^1$

David Edmunds; Amiran Gogatishvili; Tengiz Kopaliani

Construction of function spaces close to $L^\infty$ with associate space close to $L^1$

Functional Analysis 2017-10-12 v1 Analysis of PDEs Classical Analysis and ODEs

Authors: David Edmunds , Amiran Gogatishvili , Tengiz Kopaliani

Abstract

The paper introduces a variable exponent space $X$ which has in common with $L^{\infty}([0,1])$ the property that the space $C([0,1])$ of continuous functions on $[0,1]$ is a closed linear subspace in it. The associate space of $X$ contains both the Kolmogorov and the Marcinkiewicz examples of functions in $L^{1}$ with a.e. divergent Fourier series.

Keywords

variable exponent space associate space Lipschitz space Fourier series Kolmogorov example

Cite

@article{arxiv.1710.03990,
  title  = {Construction of function spaces close to $L^\infty$ with associate space close to $L^1$},
  author = {David Edmunds and Amiran Gogatishvili and Tengiz Kopaliani},
  journal= {arXiv preprint arXiv:1710.03990},
  year   = {2017}
}

Construction of function spaces close to $L^\infty$ with associate space close to $L^1$

Abstract

Keywords

Cite

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