Some remarks on Triebel spaces

Jürgen Marschall

Displaying similar documents to “Some remarks on Triebel spaces”

BMO and smooth truncation in Sobolev spaces

David Adams, Michael Frazier (1988)

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

Akihito Uchiyama (1985)

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$L^{p}$ -behaviour of the integral means of analytic functions

M. Mateljević, M. Pavlović (1984)

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The local versions of $H^{p} (ℝ^{n})$ spaces at the origin

Shan Lu, Da Yang (1995)

Studia Mathematica

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Let 0 < p ≤ 1 < q < ∞ and α = n(1/p - 1/q). We introduce some new Hardy spaces $H K ̇_{q}^{α, p} (ℝ^{n})$ which are the local versions of $H^{p} (ℝ^{n})$ spaces at the origin. Characterizations of these spaces in terms of atomic and molecular decompositions are established, together with their φ-transform characterizations in M. Frazier and B. Jawerth’s sense. We also prove an interpolation theorem for operators on $H K ̇_{q}^{α, p} (ℝ^{n})$ and discuss the $H K ̇_{q}^{α, p} (ℝ^{n})$ -boundedness of Calderón-Zygmund operators. Similar results can also be obtained...

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The φ-transform and wavelet characterizations of Herz-type spaces.

Eugenio Hernández, Guido Weiss, Dachun Yang (1996)

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In this paper, the authors establish the phi-transform and wavelet characterizations for some Herz and Herz-type Hardy spaces by means of a local version of the discrete tent spaces at the origin.

A characterization of $H^{p} (R^{n})$ in terms of atoms

Robert Latter (1978)

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Homogeneous Besov spaces on locally compact Vilenkin groups

C. Onneweer, Su Weiyi (1989)

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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...

Schauder decompositions and multiplier theorems

P. Clément, B. de Pagter, F. Sukochev, H. Witvliet (2000)

Studia Mathematica

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We study the interplay between unconditional decompositions and the R-boundedness of collections of operators. In particular, we get several multiplier results of Marcinkiewicz type for $L^{p}$ -spaces of functions with values in a Banach space X. Furthermore, we show connections between the above-mentioned properties and geometric properties of the Banach space X.