## Embeddings of Müntz spaces: The Hilbertian case

HTML articles powered by AMS MathViewer

- by S. Waleed Noor and Dan Timotin PDF
- Proc. Amer. Math. Soc.
**141**(2013), 2009-2023 Request permission

## Abstract:

Given a strictly increasing sequence $\Lambda =(\lambda _n)$ of nonnegative 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

- I. Al Alam.
*Géometrie des espaces de Müntz et opérateurs de composition $\grave {a}$ poids.*PhD thesis, Université Lille 1, 2008. - Ihab Al Alam,
*Essential norms of weighted composition operators on Müntz spaces*, J. Math. Anal. Appl.**358**(2009), no. 2, 273–280. MR**2532505**, DOI 10.1016/j.jmaa.2009.04.042 - Jöran Bergh and Jörgen Löfström,
*Interpolation spaces. An introduction*, Grundlehren der Mathematischen Wissenschaften, No. 223, Springer-Verlag, Berlin-New York, 1976. MR**0482275**, DOI 10.1007/978-3-642-66451-9 - Peter Borwein and Tamás Erdélyi,
*Polynomials and polynomial inequalities*, Graduate Texts in Mathematics, vol. 161, Springer-Verlag, New York, 1995. MR**1367960**, DOI 10.1007/978-1-4612-0793-1 - Th. J. Bromwich.
*An Introduction to the Theory of Infinite Series*. Macmillan, London, 1908. - Isabelle Chalendar, Emmanuel Fricain, and Dan Timotin,
*Embedding theorems for Müntz spaces*, Ann. Inst. Fourier (Grenoble)**61**(2011), no. 6, 2291–2311 (2012) (English, with English and French summaries). MR**2976312**, DOI 10.5802/aif.2674 - Ole Christensen,
*An introduction to frames and Riesz bases*, Applied and Numerical Harmonic Analysis, Birkhäuser Boston, Inc., Boston, MA, 2003. MR**1946982**, DOI 10.1007/978-0-8176-8224-8 - Joe Diestel, Hans Jarchow, and Andrew Tonge,
*Absolutely summing operators*, Cambridge Studies in Advanced Mathematics, vol. 43, Cambridge University Press, Cambridge, 1995. MR**1342297**, DOI 10.1017/CBO9780511526138 - Vladimir I. Gurariy and Wolfgang Lusky,
*Geometry of Müntz spaces and related questions*, Lecture Notes in Mathematics, vol. 1870, Springer-Verlag, Berlin, 2005. MR**2190706**, DOI 10.1007/11551621 - Charles A. McCarthy,
*$c_{p}$*, Israel J. Math.**5**(1967), 249–271. MR**225140**, DOI 10.1007/BF02771613 - Angela Spalsbury,
*Perturbations in Müntz’s theorem*, J. Approx. Theory**150**(2008), no. 1, 48–68. MR**2381528**, DOI 10.1016/j.jat.2007.05.002

## Additional Information

**S. Waleed Noor**- Affiliation: Abdus Salam School of Mathematical Sciences, New Muslim Town, Lahore, 54600, Pakistan
- Email: waleed_math@hotmail.com
**Dan Timotin**- Affiliation: Institute of Mathematics of the Romanian Academy, Calea Griviţei 21, Bucharest, Romania
- Email: Dan.Timotin@imar.ro
- Received by editor(s): September 18, 2011
- Published electronically: December 18, 2012
- Communicated by: Richard Rochberg
- © Copyright 2012
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc.
**141**(2013), 2009-2023 - MSC (2010): Primary 46E15, 46E20, 46E35
- DOI: https://doi.org/10.1090/S0002-9939-2012-11681-8
- MathSciNet review: 3034427