Óscar Ciaurri

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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)
For most orthogonal systems and their corresponding Fourier series, the study of the almost everywhere convergence for functions in L p requires very complicated research, harder than in the case of the mean convergence. For instance, for trigonometric series, the almost everywhere convergence for functions in L 2 is the celebrated Carleson theorem, proved(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)