Translation invariant operators on Lorentz spaces

Leonardo Colzani

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

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Ryotaro Sato (1996)

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We give a counterexample showing that $\bar{(I - T *) L_{\infty}} \cap L_{\infty}^{+} = 0$ 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.

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Hardy space estimates for multilinear operators (II).

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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.

Duality and reflexivity in grand Lebesgue spaces.

Alberto Fiorenza (2000)

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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 $L i p^{(p)} α (W) (1 \geq p \geq \infty, α > 0)$ 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...

Characterization of $H^{p} (R^{n})$ in terms of generalized Littlewood-Paley g-functions

Akihito Uchiyama (1985)

Studia Mathematica

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