# Article

 Title: A new proof of weighted weak-type inequalities for fractional integrals  (English) Author: Cruz-Uribe, D., SFO Language: English Journal: Commentationes Mathematicae Universitatis Carolinae ISSN: 0010-2628 (print) ISSN: 1213-7243 (online) Volume: 42 Issue: 3 Year: 2001 Pages: 481-485 . Category: math . Summary: We give a new and simpler proof of a two-weight, weak $(p,p)$ inequality for fractional integrals first proved by Cruz-Uribe and Pérez [4]. Keyword: weights Keyword: weak-type inequalities Keyword: fractional integrals MSC: 42B20 MSC: 42B25 idZBL: Zbl 1055.42006 idMR: MR1860236 . Date available: 2009-01-08T19:11:56Z Last updated: 2012-04-30 Stable URL: http://hdl.handle.net/10338.dmlcz/119262 . Reference: [1] Cruz-Uribe D., SFO: New proofs of two-weight norm inequalities for the maximal operator.Georgian Math. J. 7 (2000), 33-42. MR 1768043 Reference: [2] Cruz-Uribe D., SFO, Fiorenza A.: The $A_\infty$ property for Young functions and weighted norm inequalities.Houston J. Math., to appear. MR 1876947 Reference: [3] Cruz-Uribe D., SFO, Pérez C.: Sharp two-weight, weak-type norm inequalities for singular integral operators.Math. Res. Lett. 6 (1999), 417-428. MR 1713140 Reference: [4] Cruz-Uribe D., SFO, Pérez C.: Two-weight, weak-type norm inequalities for fractional integrals, Calderón-Zygmund operators and commutators.Indiana Math. J. 49 (2000), 697-721. MR 1793688 Reference: [5] García-Cuerva J., Rubio de Francia J.L.: Weighted Norm Inequalities and Related Topics.North Holland Math. Studies 116, North Holland, Amsterdam, 1985. MR 0848147 Reference: [6] Muckenhoupt B., Wheeden R.: Weighted norm inequalities for fractional integrals.Trans. Amer. Math. Soc. 192 (1974), 261-274. Zbl 0289.26010, MR 0340523 Reference: [7] Pérez C.: Two weighted inequalities for potential and fractional type maximal operators.Indiana Math. J. 43 (1994), 663-683. MR 1291534 Reference: [8] Sawyer E.T.: Weighted norm inequalities for fractional maximal operators.1980 Seminar on Harmonic Analysis, CMS Conf. Proc. 1, pp.283-309, Amer. Math. Soc., Providence, 1981. Zbl 0546.42018, MR 0670111 Reference: [9] Sawyer E.T., Wheeden R.: Weighted inequalities for fractional integrals on Euclidean and homogeneous spaces.Amer. J. Math. 114 (1992), 813-874. Zbl 0783.42011, MR 1175693 .

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