HARDY'S INEQUALITIES FOR HERMITE AND LAGUERRE EXPANSIONS

YUICHI KANJIN

doi:10.1112/S0024609396002627

Abstract

The well-known inequality of Hardy for Fourier coefficients of functions f(t)∼[sum ]∞n=−∞bneint in the real Hardy space is [sum ]∞n= −∞[mid ]bn[mid ]/([mid ]n[mid ]+1)<∞. We shall establish analogues of this inequality for the Hermite function expansions and also for the Laguerre function expansions.

Crossref Citations

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Radha, R. Naidu, D. Venku and Rudnev, Misha 2008. Image of Lp(ℝn) under the Hermite Semigroup. International Journal of Mathematics and Mathematical Sciences, Vol. 2008, Issue. 1,

Assal, Miloud 2011. Hardy's type inequality associated with the Hankel transform for over-critical exponent. Integral Transforms and Special Functions, Vol. 22, Issue. 1, p. 45.

KANJIN, Yuichi 2011. Hardy's inequalities for Hermite and Laguerre expansions revisited. Journal of the Mathematical Society of Japan, Vol. 63, Issue. 3,

Assal, Miloud and Rahmouni, Atef 2013. Hardy's type inequality associated with the Laguerre Fourier transform. Integral Transforms and Special Functions, Vol. 24, Issue. 2, p. 156.

Miloud, Assal and Atef, Rahmouni 2013. An improved Hardy’s inequality associated with the Laguerre Fourier transform. Collectanea Mathematica, Vol. 64, Issue. 2, p. 283.

Li, Zhongkai and Shi, Yehao 2014. Multipliers of Hardy Spaces Associated with Generalized Hermite Expansions. Constructive Approximation, Vol. 39, Issue. 3, p. 517.

Assal, Miloud and Rahmouni, Atef 2014. Hardy's type inequality for the over critical exponent associated with the inverse Fourier Laguerre transform. Integral Transforms and Special Functions, Vol. 25, Issue. 3, p. 173.

Mejjaoli, Hatem 2015. Hardy-type inequalities associated with the Weinstein operator. Journal of Inequalities and Applications, Vol. 2015, Issue. 1,

Li, Zhongkai Yu, Yufeng and Shi, Yehao 2015. The Hardy Inequality for Hermite Expansions. Journal of Fourier Analysis and Applications, Vol. 21, Issue. 2, p. 267.

SHI, Yehao and LI, Zhongkai 2016. Coefficient multipliers of $H^1$ into $\ell^q$ associated with Laguerre expansions. Journal of the Mathematical Society of Japan, Vol. 68, Issue. 2,

SHI, Yehao and LI, Zhongkai 2016. Multipliers of Hardy spaces associated with Laguerre expansions. Journal of the Mathematical Society of Japan, Vol. 68, Issue. 1,

Xiao, Jinsen and He, Jianxun 2017. Hardy’s inequalities for the twisted convolution with Laguerre functions. Journal of Inequalities and Applications, Vol. 2017, Issue. 1,

Xiao, Jinsen He, Jianxun and Fan, Xingya 2018. Hardy’s Inequalities for the Heisenberg Group. Potential Analysis,

Plewa, Paweł 2019. Hardy’s Inequality for Laguerre Expansions of Hermite Type. Journal of Fourier Analysis and Applications, Vol. 25, Issue. 4, p. 1855.

Plewa, Paweł 2020. Sharp Hardy’s inequality for Jacobi and symmetrized Jacobi trigonometric expansions. Journal of Approximation Theory, Vol. 256, Issue. , p. 105422.

Plewa, Paweł 2020. On Hardy's Inequality for Hermite Expansions. Taiwanese Journal of Mathematics, Vol. 24, Issue. 2,

PLEWA, Paweł 2022. Sharp Hardy's type inequality for Laguerre expansions. Journal of the Mathematical Society of Japan, Vol. 74, Issue. 2,

Plewa, Paweł 2024. Sharp Hardy’s Inequality for Orthogonal Expansions in $$H^p$$ Spaces. Journal of Fourier Analysis and Applications, Vol. 30, Issue. 1,

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HARDY'S INEQUALITIES FOR HERMITE AND LAGUERRE EXPANSIONS

Abstract

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HARDY'S INEQUALITIES FOR HERMITE AND LAGUERRE EXPANSIONS

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