The property of weak type (p,p) for the Hardy-Littlewood maximal operator and derivation of integrals
Baldomero Rubio (1976)
Studia Mathematica
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Baldomero Rubio (1976)
Studia Mathematica
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Baldomero Rubio (1975)
Collectanea Mathematica
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Soulaymane Korry (2001)
Collectanea Mathematica
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Norberto Fava (1984)
Studia Mathematica
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Miguel de Guzmán (1974)
Studia Mathematica
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Terasawa, Yutaka (2006)
Journal of Inequalities and Applications [electronic only]
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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.
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).
K. Hare, A. Stokolos (2000)
Colloquium Mathematicae
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The properties of rare maximal functions (i.e. Hardy-Littlewood maximal functions associated with sparse families of intervals) are investigated. A simple criterion allows one to decide if a given rare maximal function satisfies a converse weak type inequality. The summability properties of rare maximal functions are also considered.
Luis Caffarelli, Calixto Calderón (1974)
Studia Mathematica
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Keng Hao Ooi (2022)
Czechoslovak Mathematical Journal
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We characterize the Choquet integrals associated to Bessel capacities in terms of the preduals of the Sobolev multiplier spaces. We make use of the boundedness of local Hardy-Littlewood maximal function on the preduals of the Sobolev multiplier spaces and the minimax theorem as the main tools for the characterizations.
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...