The Hausdorff–Young Inequality and Hermite Based Triebel–Lizorkin Spaces

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Key Points

To formulate the Hausdorff–Young inequality within the framework of Hermite-based Triebel–Lizorkin spaces, particularly focusing on orthogonal expansions adapted to exponential weights.
Investigated orthogonal expansions related to exponential weights.
Utilized estimates of Kasuga and Sakai for generalized Hermite functions.
Applied interpolation techniques involving Orlicz–Lorentz spaces.
Derived inequalities in various function spaces like L^p, Lorentz, and Orlicz.
Presented a general Hausdorff–Young inequality for generalized Freud coefficients.
Formulated Hausdorff–Young inequalities in L^p, Lorentz, and Orlicz spaces.
Estimates demonstrated tighter bounds for generalized Hermite functions.
Introduced new results on Hausdorff–Young inequalities for generalized Freud coefficients.

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Calderón et al. (2026) studied this question.

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