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References
Benedek, A., andPanzone, R., The spacesL p with mixed norms.Duke Math. J. 28 (1961), 301–324.
——Calderón, A. P., andPanzone, R., Convolution operators on Banach space valued functions.Proc. Nat. Acad. Sci. U.S.A. 48 (1962), 356–365.
Calderón, A. P., A general ergodie theorem.Ann. of Math. 58 (1953), 182–191.
——, Intermediate spaces and interpolation, the complex method.Studia Math. 24 (1964), 113–190.
Calderón, A. P., Weiss, M., andZygmund, A., On the existence of singular integrals.Proc. Symposia in Pure Math. 10 A.M.S., 1967, 56–73.
——, On the existence of certain singular integrals.Acta Math. 88 (1952), 85–139.
de Guzman, M.,Singular integral operators with generalized homogeneity. Dissertation, University of Chicago, 1968.
Edwards, R. E., andHewitt, E., Pointwise limits for sequences of convolution operators.Acta Math. 113 (1965), 181–218.
Fabes, E. B. andRivière, N. M., Singular integrals with mixed homogeneity.Studia Math. 27 (1966), 19–38.
Fava, N.,Weak type inequalities for iterated operators. Dissertation, University of Minnesota, 1969.
Herz, C. S., On the mean inversion of Fourier and Hankel transforms.Proc. Nat. Acad. Sci. U.S.A. 40 (1954), 996–999.
Hörmander, L., Estimates for translation invariant operators inL p spaces.Acta Math. 104 (1960), 93–139.
Jessen, B., Marcinkiewicz, J., andZygmund, A., A note on the differentiability of multiple integrals.Fund. Math. 25 (1935), 217–234.
John, F., Extremum problems with subsidiary conditions.Studies and Essays, Interscience, 1948, 187–204.
Jones, B. F. Jr., A class of singular integrals.Amer. J. Math. 86 (1964), 441–462.
Lewis, J. E., Mixed estimates for singular integrals and an application to initial value problems in parabolic differential equations.Proc. Symposia in Pure Math. 10, A.M.S. 1967, 218–242.
Korányi, A., andVagi, I., Intégrales singulières sur certains espaces homogènes.C. R. Acad. Sci. Paris Sér. A-B. 268 (1969), 765–768.
Littman, W., McCarthy, C., andRivière, N. M.,L p-multiplier theorems.Studia Math. 30 (1968), 193–217.
———, The non-existence ofL p-estimates for certain translation-invariant operators.Studia Math. 30 (1968), 219–229.
Marcinkiewicz, J., Sur l'interpolation d'opérations.C. R. Acad. Sci. Paris Sér. A-B. 208 (1939), 1272–1273. AlsoCollected papers, Warsaw 1969, 539–540.
——, Sur les multiplicateurs des séries de Fourier.Studia Math. 8 (1938), 501–512. AlsoCollected papers. Warsaw 1964, 501–512.
Morse, A. P., A theory of covering and differentiation.Trans. Amer. Math. Soc. 55 (1944), 205–235.
——, Perfect blankets.Trans. Amer. Math. Soc. 61 (1947), 418–442.
Riesz, F. andNagy, B. Sz.,Lecons d'analyse fonctionnelle. Budapest, 1953.
Rivière, N. M., Vector valued multipliers and applications.Bull. Amer. Math. Soc. 74 (1968), 946–948.
——, On singular integrals.Bull. Amer. Math. Soc. 75 (1969), 843–847.
Schwartz, J. T., A remark on inequalities of Calderon-Zygmund type.Comm. Pure Appl. Math. 14 (1961), 785–799.
Stein, E. M. andWeiss, G., An extension of a theorem of Marcinkiewicz and some of its applications.J. Math. Mech. 8 (1959), 263–284.
Zygmund, A.,Trigonometric Series, 2nd ed., Vol. 2, Cambridge, 1959.
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The research represented in this paper was sponsored in part by the National Science Foundation grant GP 15832.
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Rivière, N.M. Singular integrals and multiplier operators. Ark. Mat. 9, 243–278 (1971). https://doi.org/10.1007/BF02383650
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DOI: https://doi.org/10.1007/BF02383650