Displaying similar documents to “Norm inequalities for the minimal and maximal operator, and differentiation of the integral.”

The one-sided minimal operator and the one-sided reverse Holder inequality

David Cruz-Uribe, SFO, C. Neugebauer, V. Olesen (1995)

Studia Mathematica

Similarity:

We introduce the one-sided minimal operator, m + f , which is analogous to the one-sided maximal operator. We determine the weight classes which govern its two-weight, strong and weak-type norm inequalities, and show that these two classes are the same. Then in the one-weight case we use this class to introduce a new one-sided reverse Hölder inequality which has several applications to one-sided ( A p + ) weights.

Two weighted inequalities for convolution maximal operators.

Ana Lucía Bernardis, Francisco Javier Martín-Reyes (2002)

Publicacions Matemàtiques

Similarity:

Let φ: R → [0,∞) an integrable function such that φχ = 0 and φ is decreasing in (0,∞). Let τf(x) = f(x-h), with h ∈ R {0} and f(x) = 1/R f(x/R), with R > 0. In this paper we characterize the pair of weights (u, v) such that the operators Mf(x) = sup|f| * [τφ](x) are of weak type (p, p) with respect to (u, v), 1 < p < ∞.

Norm inequalities for off-centered maximal operators.

Richard L. Wheeden (1993)

Publicacions Matemàtiques

Similarity:

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.

On boundedness properties of certain maximal operators

M. Menárguez (1995)

Colloquium Mathematicae

Similarity:

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.

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

Y. Rakotondratsimba (1995)

Publicacions Matemàtiques

Similarity:

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.