Embeddings of Müntz spaces: the Hilbertian case

Abstract

Given a strictly increasing sequence $\Lambda =({\lambda }_n)$ of nonegative real numbers, with ${\sum }_{n=1}^{\infty }\frac{1}{{\lambda }_n}<\infty$, the Müntz spaces $M_{\Lambda }^p$ are defined as the closure in $L^p([0,1])$ of the monomials $x^{{\lambda }_n}$. We discuss properties of the embedding $M_{\Lambda }^p\subset L^p(\mu )$, where $\mu$ is a finite positive Borel measure on the interval $[0,1]$. Most of the results are obtained for the Hilbertian case $p=2$, in which we give conditions for the embedding to be bounded, compact, or to belong to the Schatten--von Neumann ideals.

References in corpus (1)

• Embedding Theorems for Müntz spaces