Displaying similar documents to “Distribution and rearrangement estimates of the maximal function and interpolation”

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.

Norm inequalities for off-centered maximal operators.

Richard L. Wheeden (1993)

Publicacions Matemàtiques

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Sufficient conditions are derived in order that there exist strong-type weighted norm inequalities for some off-centered maximal functions. The maximal functions are of Hardy-Littlewood and fractional types taken over starlike sets in R. The sufficient conditions are close to necessary and extend some previously known weak-type results.

Improved Muckenhoupt-Wheeden inequality and weighted inequalities for potential operators.

Y. Rakotondratsimba (1995)

Publicacions Matemàtiques

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By a variant of the standard good λ inequality, we prove the Muckenhoupt-Wheeden inequality for measures which are not necessarily in the Muckenhoupt class. Moreover we can deal with a general potential operator, and consequently we obtain a suitable approach to the two weight inequality for such an operator when one of the weight functions satisfies a reverse doubling condition.

A sharp rearrangement inequality for the fractional maximal operator

A. Cianchi, R. Kerman, B. Opic, L. Pick (2000)

Studia Mathematica

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We prove a sharp pointwise estimate of the nonincreasing rearrangement of the fractional maximal function of ⨍, M γ ⨍ , by an expression involving the nonincreasing rearrangement of ⨍. This estimate is used to obtain necessary and sufficient conditions for the boundedness of M γ between classical Lorentz spaces.

Norm inequalities for the minimal and maximal operator, and differentiation of the integral.

David Cruz-Uribe, Christoph J. Neugebauer, Victor Olesen (1997)

Publicacions Matemàtiques

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We study the weighted norm inequalities for the minimal operator, a new operator analogous to the Hardy-Littlewood maximal operator which arose in the study of reverse Hölder inequalities. We characterize the classes of weights which govern the strong and weak-type norm inequalities for the minimal operator in the two weight case, and show that these classes are the same. We also show that a generalization of the minimal operator can be used to obtain information about the differentiability...