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arXiv · 1207.0946

Lebesgue type inequalities for quasi-greedy bases

Gustavo Garrigós·Eugenio Hernández·Timur Oikhberg
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Abstract

We show that for quasi-greedy bases in real or complex Banach spaces the error of the thresholding greedy algorithm of order N is bounded by the best N- term error of approximation times a function of N which depends on the democracy functions and the quasi-greedy constant of the basis. If the basis is democratic this function is bounded by C logN. We show with two examples that this bound is attained for quasi-greedy democratic bases.

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Gustavo Garrigós, Eugenio Hernández, Timur Oikhberg. 2012-07-04. Lebesgue type inequalities for quasi-greedy bases. https://arxiv.org/abs/1207.0946

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