Corpus ID: 119703999

On the orthogonal democratic systems in the $L^p$ spaces

@article{Kazarian2018OnTO,
  title={On the orthogonal democratic systems in the \$L^p\$ spaces},
  author={K. Kazarian and A. S. Antol{\'i}n},
  journal={arXiv: Functional Analysis},
  year={2018}
}
The concept of bidemocratic pair for a Banach space was introduced in \cite{KS:18}. We construct a family of orthonormal systems $\mathfrak{F}_{l},$ $l\in (0,\infty)$ of functions defined on $[-1,1]$ such that the pair $(\mathfrak{F}_{l},\mathfrak{F}_{l})$ is bidemocratic for $L^{p}[-1,1]$ and for $L^{p'}[-1,1]$ if $l\in (0, \frac{p}{2(p-2)}]$, where $p>2$ and $p'= \frac{p}{p-1}$. The system $\mathfrak{F}_{l}$ is not democratic for $L^{p'}[-1,1]$ when $l\in (\frac{p}{2(p-2)}, \frac{p}{p-2… Expand

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