Displaying similar documents to “Fixed points of the Hardy-Littlewood maximal operator.”

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.

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 sharp estimate for the Hardy-Littlewood maximal function

Loukas Grafakos, Stephen Montgomery-Smith, Olexei Motrunich (1999)

Studia Mathematica

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The best constant in the usual L p norm inequality for the centered Hardy-Littlewood maximal function on ℝ 1 is obtained for the class of all “peak-shaped” functions. A function on the line is called peak-shaped if it is positive and convex except at one point. The techniques we use include variational methods.