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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 p 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 p − L q bounds we also characterize weak type inequalities and… (More)
1 Known results and motivation
We introduce new ideas to treat the problem of connectivity of wavelets. We develop a method which produces intermediate paths of Tight Frame Wavelets (TFW). Using this method we prove that a large class of TFW-s, with only mild conditions on their spectrum, are arcwise connected.
We study the efficiency of greedy algorithms for N -term wavelet approximation in Orlicz spaces L(R). We compute the left and right democracy functions in terms of the fundamental function of L, recovering a recent result of Wojtaszczyk , which establishes that wavelet bases can only be greedy when L = L for some 1 < p <∞. In addition, optimal Jackson… (More)
We adapt the proof for � p (L p) Wolff inequalities in the case of plate decompositions of paraboloids, to obtain stronger � 2 (L p) versions. These are motivated by the study of Bergman projections for tube domains.
In this paper, we pursue the study of the radar ambiguity problem started in [Ja, GJP]. More precisely, for a given function u we ask for all functions v (called ambiguity partners) such that the ambiguity functions of u and v have same modulus. In some cases, v may be given by some elementary transformation of u and is then called a trivial partner of u… (More)
We show that for quasi-greedy bases in real or complex Banach spaces the error of the thresholding greedy algorithm of order N is bounded by the best N term error of approximation times a function of N which depends on the democracy functions and the quasi-greedy constant of the basis. If the basis is democratic this function is bounded by C logN . We show… (More)
Let m have compact support in (0, ∞). For 1 < p < 2d/(d + 1), we give a necessary and sufficient condition for the L p rad (R d)-boundedness of the maximal operator associated with the radial multiplier m(|ξ|). More generally we prove a similar result for maximal operators associated with multipliers of modified Hankel transforms. The result is obtained by… (More)
We study the completeness properties of the set of wavelets in L 2 (R). It is well-known that this set is not closed in the unit ball of L 2 (R). However, if one considers the metric inherited as a subspace (in the Fourier transform side) of L 2 (R, dξ) ∩ L 2 (R * , dξ |ξ|), we do obtain a complete metric space.