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

Research Article A Cohen-Type Inequality for Jacobi-Sobolev Expansions

Let μ be the Jacobi measure supported on the interval [−1, 1]. Let us introduce the Sobolev-type inner product 〈 f ,g〉 = ∫ 1 −1 f (x)g(x)dμ(x) + M f (1)g(1) + N f ′(1)g′(1), where M,N ≥ 0. In this paper we prove a Cohen-type inequality for the Fourier expansion in terms of the orthonormal polynomials associated with the above Sobolev inner product. We follow Dreseler and Soardi (1982) and Marke...

How Sharp Is Bernstein’s Inequality for Jacobi Polynomials?

Bernstein’s inequality for Jacobi polynomials P (α,β) n , established in 1987 by P. Baratella for the region R1/2 = {|α| ≤ 1/2, |β| ≤ 1/2}, and subsequently supplied with an improved constant by Y. Chow, L. Gatteschi, and R. Wong, is analyzed here analytically and, above all, computationally with regard to validity and sharpness, not only in the original region R1/2, but also in larger regions ...

Product Jacobi Expansions 3

Sharp Error Bounds for Jacobi Expansions and Gegenbauer-Gauss Quadrature of Analytic Functions

This paper provides a rigorous and delicate analysis for exponential decay of Jacobi polynomial expansions of analytic functions associated with the Bernstein ellipse. Using an argument that can recover the best estimate for the Chebyshev expansion, we derive various new and sharp bounds of the expansion coefficients, which are featured with explicit dependence of all related parameters and val...

Titchmarsh theorem for Jacobi Dini-Lipshitz functions

Our aim in this paper is to prove an analog of Younis's Theorem on the image under the Jacobi transform of a class functions satisfying a generalized Dini-Lipschitz condition in the space $mathrm{L}_{(alpha,beta)}^{p}(mathbb{R}^{+})$, $(1< pleq 2)$. It is a version of Titchmarsh's theorem on the description of the image under the Fourier transform of a class of functions satisfying the Dini-Lip...