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Hardy’s inequality for Laguerre expansions of Hermite type. (English) Zbl 1417.42030

Summary: Hardy’s inequality for Laguerre expansions of Hermite type with the index \(\alpha \in (\{-1/2\}\cup [1/2,\infty ))^d\) is proved in the multi-dimensional setting with the exponent \(3d / 4\). We also obtain the sharp analogue of Hardy’s inequality with \(L^1\) norm replacing \(H^1\) norm at the expense of increasing the exponent by an arbitrarily small value.

MSC:

42C10 Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.)
42B30 \(H^p\)-spaces
33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
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