BMO and smooth truncation in Sobolev spaces

David Adams; Michael Frazier

Displaying similar documents to “BMO and smooth truncation in Sobolev spaces”

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

Akihito Uchiyama (1985)

Studia Mathematica

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

Robert Latter (1978)

Studia Mathematica

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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...

Homogeneous Besov spaces on locally compact Vilenkin groups

C. Onneweer, Su Weiyi (1989)

Studia Mathematica

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Nonconvolution transforms with oscillating kernels that map $Ḃ_{1}^{0, 1}$ into itself

G. Sampson (1993)

Studia Mathematica

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We consider operators of the form $(Ω f) (y) = ʃ_{- \infty}^{\infty} Ω (y, u) f (u) d u$ with Ω(y,u) = K(y,u)h(y-u), where K is a Calderón-Zygmund kernel and $h \in L^{\infty}$ (see (0.1) and (0.2)). We give necessary and sufficient conditions for such operators to map the Besov space $Ḃ_{1}^{0, 1}$ (= B) into itself. In particular, all operators with $h (y) = e^{{i | y |}^{a}}$ , a > 0, a ≠ 1, map B into itself.

Continuity properties for the maximal operator associated with the commutator of the Bochner-Riesz operator.

Zongguang Liu, Guozhen Lu, Shanzhen Lu (2003)

Publicacions Matemàtiques

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In this paper, we obtain some strong and weak type continuity properties for the maximal operator associated with the commutator of the Bochner-Riesz operator on Hardy spaces, Hardy type spaces and weak Hardy type spaces.

Several characterizations for the special atom spaces with applications.

Geraldo Soares de Souza, Richard O&#039;Neil, Gary Sampson (1986)

Revista Matemática Iberoamericana

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The theory of functions plays an important role in harmonic analysis. Because of this, it turns out that some spaces of analytic functions have been studied extensively, such as H-spaces, Bergman spaces, etc. One of the major insights that has developed in the study of H-spaces is what we call the real atomic characterization of these spaces.

Regularity results for non-linear elliptic systems in two dimensions

Jana Stará (1971)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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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.

Some theorems on orthogonal functions (1)

R. Paley (1931)

Studia Mathematica

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