Gustavo Garrigós

Learn More
We study N-term approximation for general families of sequence spaces, establishing sharp versions of Jackson and Bernstein inequalities. The sequence spaces used are adapted to provide characterizations of Triebel-Lizorkin and Besov spaces by means of wavelet-like systems using general dilation matrices, and thus they include spaces of anisotropic(More)
We give characterizations of radial Fourier multipliers as acting on radial L functions, 1 < p < 2d/(d + 1), in terms of Lebesgue space norms for Fourier localized pieces of the convolution kernel. This is a special case of corresponding results for general Hankel multipliers. Besides L −L bounds we also characterize weak type inequalities and intermediate(More)
We prove optimal embeddings for nonlinear approximation spaces Aq , in terms of weighted Lorentz sequence spaces, with the weights depending on the democracy functions of the basis. As applications we recover known embeddings for N -term wavelet approximation in L, Orlicz, and Lorentz norms. We also study the “greedy classes” G α q introduced by Gribonval(More)
An important inequality due to Wolff on plate decompositions of cone multipliers is known to have consequences for sharp L results on cone multipliers, local smoothing for the wave equation, convolutions with radial kernels, Bergman projections in tubes over cones, averages over finite type curves in R and associated maximal functions. We observe that the(More)
We observe that the range of p for Wolff’s inequality on plate decompositions of cone multipliers can be improved by using bilinear restriction techniques. This in turn is known to improve the range for sharp Lp results on cone multipliers, local smoothing for the wave equation, convolutions with radial kernels, Bergman projections in tubes over cones,(More)