×
Muckenhoupt, Benjamin; Wheeden, Richard L.

Weighted norm inequalities for fractional integrals. (English) Zbl 0289.26010

Trans. Am. Math. Soc. 192, 261-274 (1974).
Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
scan of Zbl 0289.26010

Cited in 11 Reviews
Cited in 341 Documents

MSC:

26A33 Fractional derivatives and integrals
26D15 Inequalities for sums, series and integrals
Cite Review PDF
Full Text: DOI

References:

[1] R. R. Coifman and C. Fefferman, Weighted norm inequalities for maximal functions and singular integrals, Studia Math. 51 (1974), 241 – 250. · Zbl 0291.44007
[2] Miguel de Guzmán, A covering lemma with applications to differentiability of measures and singular integral operators, Studia Math. 34 (1970), 299 – 317. (errata insert). · Zbl 0192.48804
[3] C. Fefferman and E. M. Stein, \?^{\?} spaces of several variables, Acta Math. 129 (1972), no. 3-4, 137 – 193. · Zbl 0257.46078 · doi:10.1007/BF02392215
[4] Richard A. Hunt, On \?(\?,\?) spaces, Enseignement Math. (2) 12 (1966), 249 – 276. · Zbl 0181.40301
[5] Richard Hunt, Benjamin Muckenhoupt, and Richard Wheeden, Weighted norm inequalities for the conjugate function and Hilbert transform, Trans. Amer. Math. Soc. 176 (1973), 227 – 251. · Zbl 0262.44004
[6] G. H. Hardy and J. E. Littlewood, Some properties of fractional integrals. I, Math. Z. 27 (1928), no. 1, 565 – 606. · JFM 54.0275.05 · doi:10.1007/BF01171116
[7] Benjamin Muckenhoupt, Weighted norm inequalities for the Hardy maximal function, Trans. Amer. Math. Soc. 165 (1972), 207 – 226. · Zbl 0236.26016
[8] S. Sobolev, On a theorem in functional analysis, Mat. Sb. 4 (46) (1938), 471-497; English transl., Amer. Math. Soc. Transl. (2) 34 (1963), 39-68.
[9] Elias M. Stein, Singular integrals and differentiability properties of functions, Princeton Mathematical Series, No. 30, Princeton University Press, Princeton, N.J., 1970. · Zbl 0207.13501
[10] E. M. Stein and Guido Weiss, Fractional integrals on \?-dimensional Euclidean space, J. Math. Mech. 7 (1958), 503 – 514. · Zbl 0082.27201
[11] E. M. Stein and A. Zygmund, Boundedness of translation invariant operators on Hölder spaces and \?^{\?}-spaces, Ann. of Math. (2) 85 (1967), 337 – 349. · Zbl 0172.40102 · doi:10.2307/1970445
[12] T. Walsh, On weighted norm inequalities for fractional and singular integrals., Canad. J. Math. 23 (1971), 907 – 928. · Zbl 0221.44006 · doi:10.4153/CJM-1971-100-1
[13] A. Zygmund, Trigonometric series: Vols. I, II, Second edition, reprinted with corrections and some additions, Cambridge University Press, London-New York, 1968.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.