Finite Hilbert transforms in $L^p$
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- by R. K. Juberg PDF
- Bull. Amer. Math. Soc. 78 (1972), 435-438
References
- Paul L. Butzer and Walter Trebels, Hilberttransformation, gebrochene Integration und Differentiation, Forschungsberichte des Landes Nordrhein-Westfalen, No. 1889, Westdeutscher Verlag, Cologne, 1968 (German). MR 0236631, DOI 10.1007/978-3-663-07257-7
- R. K. Juberg, On the boundedness of certain singular integral operators, Hilbert space operators and operator algebras (Proc. Internat. Conf., Tihany, 1970) Colloq. Math. Soc. János Bolyai, vol. 5, North-Holland, Amsterdam, 1972, pp. 305–318. MR 0361932
- G. K. Kalisch, On fractional integrals of pure imaginary order in $L_{p}$, Proc. Amer. Math. Soc. 18 (1967), 136–139. MR 216310, DOI 10.1090/S0002-9939-1967-0216310-8
- W. Koppelman and J. D. Pincus, Spectral representations for finite Hilbert transformations, Math. Z. 71 (1959), 399–407. MR 107144, DOI 10.1007/BF01181411
- E. R. Love, Fractional derivatives of imaginary order, J. London Math. Soc. (2) 3 (1971), 241–259. MR 273322, DOI 10.1112/jlms/s2-3.2.241
- S. G. Mikhlin, Integral equations and their applications to certain problems in mechanics, mathematical physics and technology, Pergamon Press, New York-London-Paris-Los Angeles, 1957. Translated from the Russian by A. H. Armstrong. MR 0087877
- N. I. Muskhelishvili, Singular integral equations, Wolters-Noordhoff Publishing, Groningen, 1972. Boundary problems of functions theory and their applications to mathematical physics; Revised translation from the Russian, edited by J. R. M. Radok; Reprinted. MR 0355494
- A. S. Peters, Abel’s equation and the Cauchy integral equation of the second kind, Comm. Pure Appl. Math. 21 (1968), 51–65. MR 223839, DOI 10.1002/cpa.3160210105 9. S. G. Samko, a) A generalized Abel equation and fractional integration operators, Differencial’nye Uravnenija 4 (1968), 298-314. (Russian) MR 37 #3295. S. G. Samko, b) Noether’s theory for the generalized Abel integral equation, ibid. 4 (1968), 315-326. (Russian) MR 37 #3296.
- Eliahu Shamir, Reduced Hilbert transforms and singular integral equations, J. Analyse Math. 12 (1964), 277–305. MR 165328, DOI 10.1007/BF02807437
- F. G. Tricomi, On the finite Hilbert transformation, Quart. J. Math. Oxford Ser. (2) 2 (1951), 199–211. MR 43258, DOI 10.1093/qmath/2.1.199
- Harold Widom, Singular integral equations in $L_{p}$, Trans. Amer. Math. Soc. 97 (1960), 131–160. MR 119064, DOI 10.1090/S0002-9947-1960-0119064-7
- L. von Wolfersdorf, Zur Lösung der verallgemeinerten Abelschen Integralgleichung mit konstanten Koeffizienten, Z. Angew. Math. Mech. 49 (1969), 759–761 (German). MR 256104, DOI 10.1002/zamm.19690491212
Additional Information
- Journal: Bull. Amer. Math. Soc. 78 (1972), 435-438
- MSC (1970): Primary 4730, 4635, 4515; Secondary 4450, 2643
- DOI: https://doi.org/10.1090/S0002-9904-1972-12933-1
- MathSciNet review: 0291894