On a version of Littlewood-Paley function
P. Szeptycki (1983)
Annales Polonici Mathematici
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P. Szeptycki (1983)
Annales Polonici Mathematici
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S. K. Pichorides (1990)
Colloquium Mathematicae
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Liu, Lanzhe (2003)
Lobachevskii Journal of Mathematics
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Leonardo Colzani, Javier Pérez Lázaro (2010)
Colloquium Mathematicae
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We prove that peak shaped eigenfunctions of the one-dimensional uncentered Hardy-Littlewood maximal operator are symmetric and homogeneous. This implies that the norms of the maximal operator on L(p) spaces are not attained.
Guanghui Lu, Dinghuai Wang (2023)
Czechoslovak Mathematical Journal
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We study the mapping property of the commutator of Hardy-Littlewood maximal function on Triebel-Lizorkin spaces. Also, some new characterizations of the Lipschitz spaces are given.
Dmitry V. Rutsky (2014)
Studia Mathematica
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The Coifman-Fefferman inequality implies quite easily that a Calderón-Zygmund operator T acts boundedly in a Banach lattice X on ℝⁿ if the Hardy-Littlewood maximal operator M is bounded in both X and X'. We establish a converse result under the assumption that X has the Fatou property and X is p-convex and q-concave with some 1 < p, q < ∞: if a linear operator T is bounded in X and T is nondegenerate in a certain sense (for example, if T is a Riesz transform) then M is bounded...
Robert Fefferman (1986)
Revista Matemática Iberoamericana
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Clearly, one of the most basic contributions to the fields of real variables, partial differential equations and Fourier analysis in recent times has been the celebrated theorem of Calderón and Zygmund on the boundedness of singular integrals on R [1].
Soulaymane Korry (2002)
Revista Matemática Complutense
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We describe a class O of nonlinear operators which are bounded on the Lizorkin-Triebel spaces F (R), for 0 < s < 1 and 1 < p, q < ∞. As a corollary, we prove that the Hardy-Littlewood maximal operator is bounded on F (R), for 0 < s < 1 and 1 < p, q < ∞ ; this extends the result of Kinnunen (1997), valid for the Sobolev space H (R).
Wu, Changhong, Liu, Lanzhe (2006)
Lobachevskii Journal of Mathematics
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Carlos Pérez (1997)
The journal of Fourier analysis and applications [[Elektronische Ressource]]
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Luis Caffarelli, Calixto Calderón (1974)
Studia Mathematica
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Soulaymane Korry (2001)
Collectanea Mathematica
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Martha Guzmán-Partida (2013)
Archivum Mathematicum
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We consider central versions of the space studied by Coifman and Rochberg and later by Bennett, as well as some natural relations with a central version of a maximal operator.