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Let Jµ denote the Bessel function of order µ. The functions x −α/2−β/2−1/2 J α+β+2n+1 (x 1/2), n = 0, 1, 2,. .. , form an orthogonal system in L 2 ((0, ∞), x α+β dx) when α + β > −1. In this paper we analyze the range of p, α and β for which the Fourier series with respect to this system converges in the L p ((0, ∞), x α dx)-norm. Also, we describe the(More)
In this paper, we develop a thorough analysis of the boundedness properties of the maximal operator for the Bochner-Riesz means related to the Fourier-Bessel expansions. For this operator, we study weighted and un-weighted inequalities in the spaces L p ((0, 1), x 2ν+1 dx). Moreover, weak and restricted weak type inequalities are obtained for the critical(More)
We study an extension of the classical Paley-Wiener space structure, which is based on bilinear expansions of integral kernels into biorthogonal sequences of functions. The structure includes both sampling expansions and Fourier-Neumann type series as special cases. Concerning applications, several new results are obtained. From the Dunkl analogue of(More)