$L^p$-Convergence of Fourier-Heckman-Opdam Expansions

Abstract

We study the $L^p$-convergence of Fourier expansions in terms of non-symmetric Heckman-Opdam polynomials of type $A_1$. Using kernel estimates and duality arguments, we prove that the partial sums converge in $ L^p([-\pi,\pi],dm_k)$ for $$2-\frac{1}{k+1} < p < 2+\frac{1}{k}.$$