Sampling discretization of integral norms

@article{Dai2020SamplingDO,
  title={Sampling discretization of integral norms},
  author={Feng Dai and A. V. Prymak and Alexei Shadrin and Vladimir N. Temlyakov and Sergei Yur'evich Tikhonov},
  journal={ArXiv},
  year={2020},
  volume={abs/2001.09320}
}
The paper is devoted to discretization of integral norms of functions from a given finite dimensional subspace. Even though this problem is extremely important in applications, its systematic study has begun recently. In this paper we obtain a conditional theorem for all integral norms $L_q$, $1\le q<\infty$, which is an extension of known results for $q=1$. To discretize the integral norms successfully, we introduce a new technique, which is a combination of probabilistic technique with… 
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