On Clarkson's inequality,type and cotype for the Edmunds-Triebel logarithmic spaces |
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| Authors: | L. Y. Nikolova L. E. Persson T. Zachariades |
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| Affiliation: | 1.Department of Mathematics, Sofia University, blv. J. Bouchier 5, Sofia, 1164, Bulgaria, e-mail: ludmilan@fmi.uni-sofia.bg ,BG;2.Department of Mathematics, Lule? University of Technology, S-97187 Lule?, Sweden, e-mail: larserik@sm.luth.se ,SE;3.Department of Mathematics, University of Athens Panepistimiopolis, 15784 Athens, Greece, e-mail: tzaharia@math.uoa.gr ,GR |
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| Abstract: | We show that the (p, p') Clarkson's inequality holds in the Edmunds-Triebel logarithmic spaces Aq(logA)b,q A_{theta}({log}A)_{b,q} and in the Zygmund spaces Lp(logL)b(W) L_p({log}L)_b(Omega) , for b ? mathbbR b in mathbb{R} and for suitable 1 ￡ p ￡ 2 1 leq p leq 2 . As a consequence of these results we also obtain some new information about the types and the cotypes of these spaces. |
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