Geodesic
A Characterization of two Weight Norm Inequalities for One-Sided Operators of Fractional Type
Canadian journal of mathematics, Tome 49 (1997) no. 5, pp. 1010-1033

Voir la notice de l'article provenant de la source Cambridge University Press

In this paper we give a characterization of the pairs of weights (ω, v) such that T maps Lp(v) into Lq(ω),where T is a general one-sided operator that includes as a particular case theWeyl fractional integral. As an applicationwe solve the following problem: given a weight v, when is there a nontrivial weight ω such that T maps Lp(v) into Lq(ω)?
DOI : 10.4153/CJM-1997-051-6
Mots-clés : 26A33, 42B25, Weyl fractional integral, weights 
Lorente, Maria. A Characterization of two Weight Norm Inequalities for One-Sided Operators of Fractional Type. Canadian journal of mathematics, Tome 49 (1997) no. 5, pp. 1010-1033. doi: 10.4153/CJM-1997-051-6
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Andersen, K.F. and Sawyer, E.T., Weighted norm inequalities for the Riemann-Liouville and Weyl fractional integral operators. Trans. Amer. Math. Soc. (2) 308(1988), 547–558. Google Scholar

Lorente, M. and de la Torre, A., Weighted inequalities for some one-sided operators. Proc. Amer. Math. Soc. 124(1996), 839–848. Google Scholar

Mart, F.J.ın-Reyes and de la Torre, A., Two weight norm inequalities for fractional one-sided maximal operators. Proc. Amer.Math. Soc. 117(1993), 483–489. Google Scholar

Muckenhoupt, B., Weighted norm inequalities for classical operators. Proc. Sympos. Pure Math. Amer. Math. Soc., Providence, R.I., (1) 35(1979), 69–83. Google Scholar

Muckenhoupt, B. and Wheeden, R.L., Some weighted weak-type inequalities for the Hardy-Littlewood maximal function and the Hilbert transform. Indiana Univ. Math. J. 26(1977), 801–816. Google Scholar

Sawyer, E.T.,Weighted inequalities for the one-sided Hardy-Littlewood maximal functions. Trans.Amer. Math. Soc. 297(1986), 53–61. Google Scholar

Sawyer, E.T., A characterization of two weight norm inequalities for fractional and Poisson integrals. Trans. Amer. Math. Soc. 308(1988), 533–545. Google Scholar

Sawyer, E.T., Two weight norm inequalities for certain maximal and integral operators. In: Harmonic Analysis. Lect. Notes in Math. 908 (Eds. Ricci, F. and Weiss, G.), Springer-Verlag, 1982. 102–127. Google Scholar

Sawyer, E.T. and Wheeden, R.L.,Weighted inequalities for fractional integrals on euclidean and homogeneus spaces. Amer. J.Math. 114(1992), 813–874. Google Scholar

Sawyer, E.T., Wheeden, R.L. and Zhao, S., Weighted norm inequalities for operators of potential type and fractional maximal functions. Potential Anal. 5(1996), 523–580. Google Scholar

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