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arXiv · 1906.05630

Sharp Hardy's inequality for Jacobi and symmetrized Jacobi trigonometric expansions

Paweł Plewa
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Abstract

Four Jacobi settings are considered in the context of Hardy's inequality: the trigonometric polynomials and functions, and the corresponding symmetrized systems. In the polynomial cases sharp Hardy's inequality is proved for the type parameters $\alpha,\beta\in(-1,\infty)^d$, whereas in the function systems for $\alpha,\beta\in[-1/2,\infty)^d$. The ranges of these parameters are the widest in which the corresponding orthonormal bases are composed of bounded functions. Moreover, the sharp $L^1$-analogues of Hardy's inequality are obtained with the same restrictions on the parameters $\alpha$ and $\beta$.

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Paweł Plewa. 2019-06-13. Sharp Hardy's inequality for Jacobi and symmetrized Jacobi trigonometric expansions. https://arxiv.org/abs/1906.05630

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