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)
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)
1 Known results and motivation
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.
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 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.
We compute the democracy functions associated with wavelet bases in general Lorentz spaces Λ q w and Λ q,∞ w , for general weights w and 0 < q < ∞.
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)
Analytic Besov spaces and Hardy-type inequalities in tube domains over symmetric cones. Abstract We give various equivalent formulations to the (partially) open problem about L p-boundedness of Bergman projections in tubes over cones. Namely, we show that such boundedness is equivalent to the duality identity between Bergman spaces, A p ′ = (A p) * , and… (More)
Starting from a Whitney decomposition of a symmetric cone Ω, analog to the dyadic partition [2 j , 2 j+1) of the positive real line, in this paper we develop an adapted Littlewood-Paley theory for functions with spectrum in Ω. In particular, we define a natural class of Besov spaces of such functions, B p,q ν , where the role of usual derivation is now… (More)