Embedding Theorems for Müntz spaces

Details Embedding Theorems for Müntz spaces Embedding Theorems for Müntz spaces

2010-01-18

arxiv.org/abs/1001.3013v1

Mathematics

Functional Analysis

21 pages

Scientific paper

We discuss boundedness and compactness properties of the embedding $M_\Lambda^1\subset L^1(\mu)$, where $M_\Lambda^1$ is the closure of the monomials $x^{\lambda_n}$ in $L1([0,1])$ and $\mu$ is a finite positive Borel measure on the interval $[0,1]$. In particular, we introduce a class of "sublinear" measures and provide a rather complete solution of the embedding problem for the class of quasilacunary sequences $\Lambda$. Finally, we show how one can recapture some of Al Alam's results on boundedness and essential norm of weighted composition operators from $M_\Lambda^1$ to $L1([0,1])$.

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