Displaying similar documents to “Rational algebra and MM functions”

Triebel-Lizorkin spaces on spaces of homogeneous type

Y.-S. Han (1994)

Studia Mathematica

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In [HS] the Besov and Triebel-Lizorkin spaces on spaces of homogeneous type were introduced. In this paper, the Triebel-Lizorkin spaces on spaces of homogeneous type are generalized to the case where p 0 < p ≤ 1 ≤ q < ∞ , and a new atomic decomposition for these spaces is obtained. As a consequence, we give the Littlewood-Paley characterization of Hardy spaces on spaces of homogeneous type which were introduced by the maximal function characterization in [MS2].

Smooth operators for the regular representation on homogeneous spaces

Severino Melo (2000)

Studia Mathematica

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A necessary and sufficient condition for a bounded operator on L 2 ( M ) , M a Riemannian compact homogeneous space, to be smooth under conjugation by the regular representation is given. It is shown that, if all formal ’Fourier multipliers with variable coefficients’ are bounded, then they are also smooth. In particular, they are smooth if M is a rank-one symmetric space.