Displaying similar documents to “A sharp estimate for the Hardy-Littlewood maximal function”

Eigenfunctions of the Hardy-Littlewood maximal operator

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.

Necessary and sufficient conditions for boundedness of the maximal operator in local Morrey-type spaces

Viktor I. Burenkov, Huseyn V. Guliyev (2004)

Studia Mathematica

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The problem of boundedness of the Hardy-Littewood maximal operator in local and global Morrey-type spaces is reduced to the problem of boundedness of the Hardy operator in weighted L p -spaces on the cone of non-negative non-increasing functions. This allows obtaining sufficient conditions for boundedness for all admissible values of the parameters. Moreover, in case of local Morrey-type spaces, for some values of the parameters, these sufficient conditions are also necessary.

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...

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 &lt; s &lt; 1 and 1 &lt; p, q &lt; ∞. As a corollary, we prove that the Hardy-Littlewood maximal operator is bounded on F (R), for 0 &lt; s &lt; 1 and 1 &lt; p, q &lt; ∞ ; this extends the result of Kinnunen (1997), valid for the Sobolev space H (R).

A remark on the centered n -dimensional Hardy-Littlewood maximal function

J. M. Aldaz (2000)

Czechoslovak Mathematical Journal

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We study the behaviour of the n -dimensional centered Hardy-Littlewood maximal operator associated to the family of cubes with sides parallel to the axes, improving the previously known lower bounds for the best constants c n that appear in the weak type ( 1 , 1 ) inequalities.