This is an announcement for the paper "Lebesgue type inequalities for quasi-greedy bases" by Gustavo Garrigos, Eugenio Hernandez, and Timur Oikhberg.

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.

Archive classification: math.FA

Mathematics Subject Classification: 41A65, 41A46, 41A17

Report Number: 01

Remarks: 19 pages

Submitted from: eugenio.hernandez@uam.es

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1207.0946

or

http://arXiv.org/abs/1207.0946