Displaying similar documents to “Boundedness of Hardy-Littlewood maximal operator in the framework of Lizorkin-Triebel spaces.”

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.

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...

Hardy Inequality in Variable Exponent Lebesgue Spaces

Diening, Lars, Samko, Stefan (2007)

Fractional Calculus and Applied Analysis

Similarity:

Mathematics Subject Classification: 26D10, 46E30, 47B38 We prove the Hardy inequality and a similar inequality for the dual Hardy operator for variable exponent Lebesgue spaces.