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Displaying similar documents to “Weighted weak type inequalities for certain maximal functions”

Some weighted inequalities for general one-sided maximal operators

F. Martín-Reyes, A. de la Torre (1997)

Studia Mathematica

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We characterize the pairs of weights on ℝ for which the operators M h , k + f ( x ) = s u p c > x h ( x , c ) ʃ x c f ( s ) k ( x , s , c ) d s are of weak type (p,q), or of restricted weak type (p,q), 1 ≤ p < q < ∞, between the Lebesgue spaces with the coresponding weights. The functions h and k are positive, h is defined on ( x , c ) : x < c , while k is defined on ( x , s , c ) : x < s < c . If h ( x , c ) = ( c - x ) - β , k ( x , s , c ) = ( c - s ) α - 1 , 0 ≤ β ≤ α ≤ 1, we obtain the operator M α , β + f = s u p c > x 1 / ( c - x ) β ʃ x c f ( s ) / ( c - s ) 1 - α d s . For this operator, under the assumption 1/p - 1/q = α - β, we extend the weak type characterization to the case p = q and prove that in the case of equal...

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

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

Studia Mathematica

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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

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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 &gt; 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 &lt; p &lt; ∞.

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 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...

The space Weak H¹

Robert Fefferman, Fernando Soria (1987)

Studia Mathematica

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