The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

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

Similarity:

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

Similarity:

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

Similarity:

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

Similarity:

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.