A characterization of in terms of atoms
Robert Latter (1978)
Studia Mathematica
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Robert Latter (1978)
Studia Mathematica
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C. Onneweer, Su Weiyi (1989)
Studia Mathematica
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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 which are the local versions of 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 and discuss the -boundedness of Calderón-Zygmund operators. Similar results can also be obtained...
David Adams, Michael Frazier (1988)
Studia Mathematica
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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 -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.
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.
G. Sampson (1993)
Studia Mathematica
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We consider operators of the form with Ω(y,u) = K(y,u)h(y-u), where K is a Calderón-Zygmund kernel and (see (0.1) and (0.2)). We give necessary and sufficient conditions for such operators to map the Besov space (= B) into itself. In particular, all operators with , a > 0, a ≠ 1, map B into itself.
Akihito Uchiyama (1985)
Studia Mathematica
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Jun Tateoka (1994)
Studia Mathematica
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C. Watari [12] obtained a simple characterization of Lipschitz classes on the dyadic group using the -modulus of continuity and the best approximation by Walsh polynomials. Onneweer and Weiyi [4] characterized homogeneous Besov spaces 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 by oscillations, atoms and others on the dyadic groups. As applications, we show a strong capacity inequality...
Paul Sisson (1995)
Studia Mathematica
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A rigid space is a topological vector space whose endomorphisms are all simply scalar multiples of the identity map. The first complete rigid space was published in 1981 in [2]. Clearly a rigid space is a trivial-dual space, and admits no compact endomorphisms. In this paper a modification of the original construction results in a rigid space which is, however, the domain space of a compact operator, answering a question that was first raised soon after the existence of complete rigid...
Thomas-William Korner (1978)
Annales de l'institut Fourier
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As in Part I [Annales de l’Inst. Fourier, 27-3 (1997), 97-113], our object is to construct a measure whose support has Lebesgue measure zero, but whose Fourier transform drops away extremely fast.