## Journal of the Mathematical Society of Japan

### Hardy's inequalities for Hermite and Laguerre expansions revisited

Yuichi KANJIN

#### Abstract

We show that Hardy's inequalities for Laguerre expansions hold on the space $L^1(0,\infty)$ when the Laguerre parameters $\alpha$ are positive, and we prove that although the inequality holds on the real Hardy space $H^1(0,\infty)$ if $\alpha= 0$, it does not hold on $L^1(0,\infty)$. Further, Hardy's inequality for Hermite expansion is established on $L^1(0,\infty)$.

#### Article information

Source
J. Math. Soc. Japan Volume 63, Number 3 (2011), 753-767.

Dates
First available: 1 August 2011

http://projecteuclid.org/euclid.jmsj/1312203797

Digital Object Identifier
doi:10.2969/jmsj/06330753

Zentralblatt MATH identifier
05950718

Mathematical Reviews number (MathSciNet)
MR2836741

#### Citation

KANJIN, Yuichi. Hardy's inequalities for Hermite and Laguerre expansions revisited. Journal of the Mathematical Society of Japan 63 (2011), no. 3, 753--767. doi:10.2969/jmsj/06330753. http://projecteuclid.org/euclid.jmsj/1312203797.

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