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.
Kokilashvili, Vakhtang
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Michael Christ (1984)
Studia Mathematica
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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.
Qinsheng Lai (1995)
Studia Mathematica
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Kabe Moen (2009)
Studia Mathematica
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We investigate the boundedness of the fractional maximal operator with respect to a general basis on weighted Lebesgue spaces. We characterize the boundedness of these operators for one-weight and two-weight inequalities extending the work of Jawerth. A new two-weight testing condition for the fractional maximal operator on a general basis is introduced extending the work of Sawyer for the basis of cubes. We also find the sharp dependence in the two-weight case between the operator norm...
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.
R. Coifman, C. Fefferman (1974)
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.