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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)
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)