Inequalities for $L^p$-norms that sharpen the triangle inequality and complement Hanner's Inequality

E. Carlen; R. Frank; P. Ivanisvili; E. Lieb

DOI:10.1007/s12220-020-00425-y

Corpus ID: 73582517

Inequalities for $L^p$-norms that sharpen the triangle inequality and complement Hanner's Inequality

@article{Carlen2018InequalitiesF,
  title={Inequalities for \$L^p\$-norms that sharpen the triangle inequality and complement Hanner's Inequality},
  author={E. Carlen and R. Frank and P. Ivanisvili and E. Lieb},
  journal={arXiv: Functional Analysis},
  year={2018}
}

E. Carlen, R. Frank, +1 author E. Lieb

Published 2018

Mathematics

arXiv: Functional Analysis

In 2006 Carbery raised a question about an improvement on the na\"ive norm inequality $\|f+g\|_p^p \leq 2^{p-1}(\|f\|_p^p + \|g\|_p^p)$ for two functions in $L^p$ of any measure space. When $f=g$ this is an equality, but when the supports of $f$ and $g$ are disjoint the factor $2^{p-1}$ is not needed. Carbery's question concerns a proposed interpolation between the two situations for $p>2$. The interpolation parameter measuring the overlap is $\|fg\|_{p/2}$. We prove an inequality of this type… CONTINUE READING

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