Displaying similar documents to “Translation invariant operators on Lorentz spaces”

On invariant measures for power bounded positive operators

Ryotaro Sato (1996)

Studia Mathematica

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We give a counterexample showing that ( I - T * ) L ∞ ¯ ∩ L ∞ + = 0 does not imply the existence of a strictly positive function u in L 1 with Tu = u, where T is a power bounded positive linear operator on L 1 of a σ-finite measure space. This settles a conjecture by Brunel, Horowitz, and Lin.

Hardy space estimates for multilinear operators (II).

Loukas Grafakos (1992)

Revista Matemática Iberoamericana

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We continue the study of multilinear operators given by products of finite vectors of Calderón-Zygmund operators. We determine the set of all r ≤ 1 for which these operators map products of Lebesgue spaces L(R) into the Hardy spaces H(R). At the endpoint case r = n/(n + m + 1), where m is the highest vanishing moment of the multilinear operator, we prove a weak type result.

On the characterization of Hardy-Besov spaces on the dyadic group and its applications

Jun Tateoka (1994)

Studia Mathematica

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C. Watari [12] obtained a simple characterization of Lipschitz classes L i p ( p ) α ( W ) ( 1 ≥ p ≥ ∞ , α > 0 ) on the dyadic group using the L p -modulus of continuity and the best approximation by Walsh polynomials. Onneweer and Weiyi [4] characterized homogeneous Besov spaces B p , q α on locally compact Vilenkin groups, but there are still some gaps to be filled up. Our purpose is to give the characterization of Besov spaces B p , q α by oscillations, atoms and others on the dyadic groups. As applications, we show a strong capacity inequality...