On Muckenhoupt and Sawyer conditions for maximal operators.
Y. Rakotondratsimba (1993)
Publicacions Matemàtiques
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Y. Rakotondratsimba (1993)
Publicacions Matemàtiques
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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.
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.
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...
Michael Christ (1984)
Studia Mathematica
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Kokilashvili, Vakhtang
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S. Ombrosi, L. de Rosa (2003)
Publicacions Matemàtiques
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Rafeiro, Humberto, Samko, Stefan (2007)
Fractional Calculus and Applied Analysis
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2000 Mathematics Subject Classification: 45A05, 45B05, 45E05,45P05, 46E30 We obtain a criterion of Fredholmness and formula for the Fredholm index of a certain class of one-dimensional integral operators M with a weak singularity in the kernel, from the variable exponent Lebesgue space L^p(·) ([a, b], ?) to the Sobolev type space L^α,p(·) ([a, b], ?) of fractional smoothness. We also give formulas of closed form solutions ϕ ∈ L^p(·) of the 1st kind integral equation M0ϕ =...
Tord Sjödin (1990)
Studia Mathematica
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