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Greedy Bases for Besov Spaces |
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| Authors: | S. J. Dilworth D. Freeman E. Odell T. Schlumprecht |
| Affiliation: | 1. Department of Mathematics, University of South Carolina, Columbia, SC, 29208, USA 2. Department of Mathematics, Texas A&M University, College Station, TX, 77843, USA 3. Department of Mathematics, The University of Texas, 1 University Station C1200, Austin, TX, 8712, USA |
| Abstract: | We prove that the Banach space (?n=1￥lpn)lq(bigoplus_{n=1}^{infty}ell_{p}^{n})_{ell_{q}}, which is isomorphic to certain Besov spaces, has a greedy basis whenever 1≤p≤∞ and 1<q<∞. Furthermore, the Banach spaces (?n=1￥lpn)l1(bigoplus_{n=1}^{infty}ell _{p}^{n})_{ell_{1}}, with 1<p≤∞, and (?n=1￥lpn)c0(bigoplus_{n=1}^{infty}ell_{p}^{n})_{c_{0}}, with 1≤p<∞, do not have a greedy basis. We prove as well that the space (?n=1￥lpn)lq(bigoplus_{n=1}^{infty}ell _{p}^{n})_{ell_{q}} has a 1-greedy basis if and only if 1≤p=q≤∞. |
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