Taiwanese Journal of Mathematics

On Hardy's Inequality for Hermite Expansions

Paweł Plewa

Advance publication

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Abstract

Sharp multi-dimensional Hardy's inequality for the Laguerre functions of Hermite type is proved for the type parameter $\alpha \in [-1/2,\infty)^d$. As a consequence we obtain the corresponding result for the generalized Hermite expansions. In particular, it validates that the known version of Hardy's inequality for the Hermite functions is sharp.

Article information

Source
Taiwanese J. Math., Advance publication (2019), 15 pages.

Dates
First available in Project Euclid: 5 June 2019

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1559700015

Digital Object Identifier
doi:10.11650/tjm/190601

Subjects
Primary: 42C10: Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.)
Secondary: 42B30: $H^p$-spaces 33C45: Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) [See also 42C05 for general orthogonal polynomials and functions]

Keywords
Hardy's inequality Hardy's space Hermite expansions Laguerre expansions of Hermite type

Citation

Plewa, Paweł. On Hardy's Inequality for Hermite Expansions. Taiwanese J. Math., advance publication, 5 June 2019. doi:10.11650/tjm/190601. https://projecteuclid.org/euclid.twjm/1559700015


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