Bibliography
A. P. Calderon, Intermediate spaces and interpolation, Warsaw Conference, 1960.
A. P. Calderon, Lebesgue spaces of differentiable functions,Proc. of Symposia in Pure Math., Vol. 4, Amer. Math. Soc., 1961, pp. 33–49.
I. C. Gohberg, and M. G. Krein, Basic properties of defect numbers, root numbers and indices of linear operators,Usp. Mat. Nauk, 12,2,1957, pp. 43–118. (A.M.S. translation: Ser. 2, vol. 13, pp. 185–264).
L. Hörmander, Estimates for translation invariant operators inL p spaces,Acta Math., 104, 1960, pp. 93–140.
W. Koppelman and J. V. Pincus, Spectral representations of finite Hilbert transformation,Math. Z., 71, 1959, pp. 399–407.
J. L. Lions, and E. Magenes, Problemi ai limiti non omogenei (III),Annali di Pisa, 15, 1961, pp. 39–101.
—, Problèmes aux limites non homogènes, (IV),Annali di Pisa, 15, 1961, pp. 311–326.
S. G. Mikhlin, Fourier integrals and multiple singular integrals.Vestnik Leningrad Univ., 1957, 7, pp. 143–155.
N. I. Muskhelishvili,Singular integral equations. English translation: P. Noordhof, N. V., Groningen, Holland, 1953.
M. Nikolski, On the imbedding, continuation and approximation theorems for differentiable functions in many variables,Usp. Mat. Nauk, 16, 5, 1961, pp. 63–114.
J. Peetre, Another approach to elliptic boundary problems,Comm. Pure App. Math., 14, 1961, pp. 711–731.
—, Mixed problems for higher order elliptic equations in two variables,Annali di Pisa, 15, 1961, pp. 337–353.
J. Schwartz, Some results on the spectra and spectral resolutions of a class of singular integral operators,Comm. Pure. App. Math., 15, 1962, pp. 75–90.
E. Shamir, Evaluation dansW s,p pour des problèmes aux limites elliptiques mixtes dans le plan,C. R. Acad. Sci. Paris, 254, 1962, pp. 3621–3623.
—, Mixed boundary value problems for elliptic equations in the plane—theL p theory,Annali di Pisa, 17, 1963, pp. 117–139.
—, Une propriété des espacesH s,p,C.R. Acad. Sci. Paris, 255, 1962, pp. 448–449.
H. Widom, Singular integral equations inL p,Trans. Amer. Math. Soc., 97, 1960, pp. 131–159.
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Shamir, E. Reduced Hilbert transforms and singular integral equations. J. Anal. Math. 12, 277–305 (1964). https://doi.org/10.1007/BF02807437
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DOI: https://doi.org/10.1007/BF02807437