Weak type estimates for the Hardy-Littlewood maximal functions
Luis Caffarelli, Calixto Calderón (1974)
Studia Mathematica
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Displaying similar documents to “Outer measures and weak type estimates of Hardy-Littlewood maximal operators.”
Weak type estimates for the Hardy-Littlewood maximal functions
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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.
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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.
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Boundedness of Hardy-Littlewood maximal operator in the framework of Lizorkin-Triebel spaces.
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).
A₁-regularity and boundedness of Calderón-Zygmund operators
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...
A certain modification of Hardy's inequality
B. Florkiewicz, A. Rybarski (1972)
Colloquium Mathematicae
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Mostafa A. Nasr (1977)
Annales Polonici Mathematici
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On boundedness properties of certain maximal operators
M. Menárguez (1995)
Colloquium Mathematicae
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It is known that the weak type (1,1) for the Hardy-Littlewood maximal operator can be obtained from the weak type (1,1) over Dirac deltas. This theorem is due to M. de Guzmán. In this paper, we develop a technique that allows us to prove such a theorem for operators and measure spaces in which Guzmán's technique cannot be used.