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.
Eric Sawyer (1982)
Studia Mathematica
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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 > 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 < ∞.
Alberto Criado, Fernando Soria (2016)
Studia Mathematica
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In recent work by Reguera and Thiele (2012) and by Reguera and Scurry (2013), two conjectures about joint weighted estimates for Calderón-Zygmund operators and the Hardy-Littlewood maximal function were refuted in the one-dimensional case. One of the key ingredients for these results is the construction of weights for which the value of the Hilbert transform is substantially bigger than that of the maximal function. In this work, we show that a similar construction is possible for classical...
Mark Leckband (1987)
Studia Mathematica
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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.
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...
David Cruz-Uribe, Carlos Pérez (2002)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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We give type conditions which are sufficient for two-weight, strong inequalities for Calderón-Zygmund operators, commutators, and the Littlewood-Paley square function . Our results extend earlier work on weak inequalities in [13].
Irina Asekritova, Natan Krugljak, Lech Maligranda, Lars-Erik Persson (1997)
Studia Mathematica
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There are given necessary and sufficient conditions on a measure dμ(x)=w(x)dx under which the key estimates for the distribution and rearrangement of the maximal function due to Riesz, Wiener, Herz and Stein are valid. As a consequence, we obtain the equivalence of the Riesz and Wiener inequalities which seems to be new even for the Lebesgue measure. Our main tools are estimates of the distribution of the averaging function f** and a modified version of the Calderón-Zygmund decomposition....
Y. Rakotondratsimba (1994)
Publicacions Matemàtiques
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For some pairs of weight functions u, v which satisfy the well-known Muckenhoupt conditions, we derive the boundedness of the maximal fractional operator M (0 ≤ s < n) from L to L with q < p.