A note on a theorem of Sparr

Authors

  • Y. Ameur

DOI:

https://doi.org/10.7146/math.scand.a-14435

Abstract

We prove that, regardless of the choice of a positive, concave function $\psi$ on $\mathbf{R}_{+}$ and a "weight function" $\lambda$, the weighted $\ell_2$-space $\ell_2(\psi(\lambda))$ is $c$-interpolation with respect to the couple $(\ell_2,\ell_2(\lambda))$, where $c\leq\sqrt{2}$. Our main result is that $c=\sqrt{2}$ is best possible here; a fact which is implicit in the work of G. Sparr.

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Published

2004-03-01

How to Cite

Ameur, Y. (2004). A note on a theorem of Sparr. MATHEMATICA SCANDINAVICA, 94(1), 155–160. https://doi.org/10.7146/math.scand.a-14435

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Section

Articles