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arXiv · 1802.04649

Optimal Weak Parallelogram Constants for $L^p$ Spaces

Raymond Cheng·Javad Mashreghi·William T. Ross
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Abstract

Inspired by Clarkson's inequalities for $L^p$ and continuing work from \cite{CR}, this paper computes the optimal constant $C$ in the weak parallelogram laws $$ \|f + g \|^r + C\|f - g\|^r \leq 2^{r-1}\big( \|f\|^r + \|g\|^r \big), $$ $$ \|f + g \|^r + C\|f- g \|^r \geq 2^{r-1}\big( \|f\|^r + \|g \|^r \big)$$ for the $L^p$ spaces, $1 < p < \infty$.

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Raymond Cheng, Javad Mashreghi, William T. Ross. 2018-02-13. Optimal Weak Parallelogram Constants for $L^p$ Spaces. https://arxiv.org/abs/1802.04649

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