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Lebesgue type inequalities for quasi-greedy bases
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.Comment: 19 page
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