BMO and smooth truncation in Sobolev spaces
David Adams, Michael Frazier (1988)
Studia Mathematica
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David Adams, Michael Frazier (1988)
Studia Mathematica
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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.
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...
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...
M. Mateljević, M. Pavlović (1984)
Studia Mathematica
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Chang-Pao Chen, Dah-Chin Luor (2000)
Studia Mathematica
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Let s* denote the maximal function associated with the rectangular partial sums of a given double function series with coefficients . The following generalized Hardy-Littlewood inequality is investigated: , where ξ̅=max(ξ,1), 0 < p < ∞, and μ is a suitable positive Borel measure. We give sufficient conditions on and μ under which the above Hardy-Littlewood inequality holds. Several variants of this inequality are also examined. As a consequence, the ||·||p,μ-convergence property...
Akihito Uchiyama (1985)
Studia Mathematica
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Der-Chen Chang, Song-Ying Li (1999)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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R. Paley (1931)
Studia Mathematica
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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.