Expansion by orthogonal systems with respect to Freud weights related to Hardy spaces
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Abstract:
For the basic class of Freud weights $w_\alpha (x) = \exp (-\vert x\vert ^\alpha /2), \alpha >1$ the coefficients of the expansion of $w_\alpha f\in H_p(R)$ by the Freud orthogonal system $\{w_\alpha p_{n,\alpha }\}^\infty _{n=0} ,$ where $p_{n,\alpha }$ are polynomials of degree $n,$ are related to the quasi-norm (or norm) of $w_\alpha f$ in $H_p(R).$ Relations are achieved for all $\alpha >1$ and $\frac 12 <p<1,$ and for some $\alpha$ for a larger range of $p.$ As a result, estimates for $1<p\le 2$ are also improved.References
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Additional Information
- Z. Ditzian
- Affiliation: Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, Canada T6G 2G1
- MR Author ID: 58415
- Email: zditzian@gmail.com
- Received by editor(s): January 7, 2017
- Received by editor(s) in revised form: June 5, 2017
- Published electronically: December 4, 2017
- Communicated by: Yuan Xu
- © Copyright 2017 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 146 (2018), 1665-1672
- MSC (2010): Primary 42C10, 42B30, 42C05, 26D15
- DOI: https://doi.org/10.1090/proc/13842
- MathSciNet review: 3754350