Greedy bases in L p spaces |
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Authors: | K. Kazarian V. N. Temlyakov |
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Affiliation: | 16607. Department of Mathematics, Mod. 17, Universidad Autónoma de Madrid, 28049, Madrid, Spain 26607. Mathematics Department, University of South Carolina, 1523 Greene Street, Columbia, SC, 29208, USA 36607. Steklov Mathematical Institute, ul. Gubkina 8, Moscow, 119991, Russia
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Abstract: | We consider a weighted L p space L p (w) with a weight function w. It is known that the Haar system H p normalized in L p is a greedy basis of L p , 1 < p < ∞. We study a question of when the Haar system H p w normalized in L p (w) is a greedy basis of L p (w), 1 < p < ∞. We prove that if w is such that H p w is a Schauder basis of L p (w), then H p w is also a greedy basis of L p (w), 1 < p < ∞. Moreover, we prove that a subsystem of the Haar system obtained by discarding finitely many elements from it is a Schauder basis in a weighted norm space L p (w); then it is a greedy basis. |
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