Y. Rakotondratsimba (1998)
Collectanea Mathematica
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It is proved that, for some reverse doubling weight functions, the related operator which appears in the Fefferman Stein's inequality can be taken smaller than those operators for which such an inequality is known to be true.
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...
Michael Christ (1984)
Studia Mathematica
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Steven Bloom (1990)
Studia Mathematica
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Kinnunen, Juha (1994)
Annales Academiae Scientiarum Fennicae. Series A I. Mathematica
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Jesús Bastero, Mario Milman, Francisco J. Ruiz (2000)
Revista de la Real Academia de Ciencias Exactas Físicas y Naturales
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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.
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....
Donald Krug, Alberto Torchinsky (1994)
Revista Matemática Iberoamericana
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In this paper we discuss a weighted version of Journé's covering lemma, a substitution for Whitney decomposition of an open set in R where squares are replaced by rectangles. We then apply this result to obtain a sharp version of the atomic decomposition of the weighted Hardy spaces H (R x R ) and a description of their duals when p is close to 1.
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 < ∞.
Benjamin Muckenhoupt (1974)
Studia Mathematica
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Israel P. Rivera-Ríos (2017)
Concrete Operators
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Quantitative versions of weighted estimates obtained by F. Ruiz and J.L. Torrea [30, 31] for the operator [...] are obtained. As a consequence, some sufficient conditions for the boundedness of Min the two weight setting in the spirit of the results obtained by C. Pérez and E. Rela [26] and very recently by M. Lacey and S. Spencer [17] for the Hardy-Littlewood maximal operator are derived. As a byproduct some new quantitative estimates for the Poisson integral are obtained.