Marcinkiewicz interpolation theorem and Marcinkiewicz Spaces

• Autorzy: Maligranda L.
• Konferencja: 6th European Congress of Mathematics, 2-7 July 2012 Kraków
• Języki publikacji: EN

Słowa kluczowe

EN

Marcinkiewicz Józef; Marcinkiewicz spaces; Marcinkiewicz interpolation theorem; mathematical work; scientific biography

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Wiadomości Matematyczne
• Rocznik: 2012
• Tom: T. 48, Nr 2
• Strony: 157--171
• Opis fizyczny: Bibliogr. 50 poz.

Twórcy

autor

Maligranda L.

• Department of Engineering Sciences and Mathematics, Lulea University of Technology, SE-971 87 Lulea, Sweden

Bibliografia

• [1] S.V. Astashkin, L. Maligranda, Interpolation between L1 and Lp, 1 < p < ∞, Proc. Amer. Math. Soc. 132 (2004), no. 10, 2929-2938.
• [2] C. Bennett, R. Sharpley, Interpolation of Operators, Academic Press, Boston 1988. [Marcinkiewicz interpolation theorem, pp. 216-230].
• [3] C. A. Berenstein, M. Cotlar, N. Kerzman, P. Kree, Some remarks on the Marcinkiewicz convexity theorem in the upper triangle, Studia Math. 29 (1967), 79-95.
• [4] J. Bergh, J. Lófstróm, Interpolation Spaces. An Introduction, Springer, Berlin-New York 1976. [Marcinkiewicz theorem, pp. 6-11 and application, pp. 11-12].
• [5] J.-P. Bertrandias, Espaces de fonctions bornees et continues en moyenne asymp-totique d’ordre p, Bull. Soc. Math. France Mem. 5 (1966), 1-106. [Besiko-vitch-Marcinkiewicz space Mp, pp. 12-51; Marcinkiewicz theorem on completeness, p. 12].
• [6] J.P. Bertrandias, J. Couot, J. Dhombres, M. Mendes France, V.-K. Pham Phu Hien, Kh. Vo-Khac, Espaces de Marcinkiewicz: Correlations, Measures, Systemes Dynamiques, Masson, Paris 1987. [Marcinkiewicz spaces, pp. 2-3,11,13, 59, 78].
• [7] D.W. Boyd, Indices of function spaces and their relationship to interpolation, Canad. J. Math. 21 (1969), 1245-1254.
• [8] Yu. A. Brudnyi, N. Ya. Krugljak, Interpolation Functors and Interpolation Spaces I, Norlh-Holland, Amsterdam 1991. [Marcinkiewicz theorem, pp. 66-83; Marcinkiewicz space M((p), p. 472].
• [9] A. P. Calderón, Spaces between L1 and L°° and the theorem of Marcinkiewicz, Studia Math. 26 (1966), 273-299.
• [10] A. Cianchi, An optimal interpolation theorem of Marcinkiewicz type in Orlicz spaces,J. Funct. Anal. 153 (1998), no. 2, 357-381.
• [11] C. Corduneanu, Almost Periodic Oscillations and Waves, Springer, New York 2009. [Marcinkiewicz space, pp. 41-46].
• [12] M. Cotlar, A general interpolation theorem for linear operations, Rev. Mat. Cuyana 1 (1955). 57-84 (1956).
• [13] V.I. Dmitriev, S.G. Krein, Interpolation of operators of weak type, Anal. Math. 4 (1978), no. 2, 83-99.
• [14] N. Dunfort, J.T. Schwartz, Linear Operators. Part 11: Spectral Theory. Self Adjoint Operators in Hilbert Space, John Wiley & Sons, New Yurk London 1963. [interpolation theorem of Marcinkiewicz, pp. 1166-1168].
• [15] R. E. Edwards, Fourier Series. Vol. 2. A Modern Introduction, 2nd ed., Springer, New York-Berlin 1982. [13.8. Marcinkiewicz interpolation theorem].
• [16] G.B. Folland, Real Analysis. Modern Techniques and their Applications, 2nd ed., Wiley, New York 1999. [Marcinkiewicz interpolation theorem, pp. 203-208].
• [17] J. Garcia-Cuerva, J. L. Rubio de Francia, Weighted Norm Inequalities and Related Topics, North-Holland, Amsterdam 1985. [Marcinkiewicz interpolation theorem, pp. 148-150].
• [18] D.J.H. Garling, Inequalities: A Journey into Linear Analysis, Cambridge Univ. Press, Cambridge 2007. [Marcinkiewicz interpolation theorem, pp. 154-156 and 162-165].
• [19] L. Grafakos, Classical Fourier Analysis, 2nd ed., Springer, New York 2008. [Marcinkiewicz interpolation theorem, pp. 31-34 and off-diagonal Marcinkiewicz interpolation theorem, pp. 55-63].
• [20] J. Horvath, Encounters with Mischa Cotlar, Notices Amer. Math. Soc. 56 (2009), no. 5, 616-620.
• [21] R. A. Hunt, An extension of the Marcinkiewicz interpolation theorem to Lorentz spaces, Bull. Amer. Math. Soc. 70 (1964), 803-807.
• [22] B. S. Kashin, A. A. Saakyan, Orthogonal Series, Nauka, Moscow 1984. (Russian) [Appendix 1.2. Marcinkiewicz interpolation theorem, pp. 442-443]; English transl. AMS, Providence 1989 [Appendix 2.1. Marcinkiewicz interpolation theorem, pp. 390-392].
• [23] S. G. Krein, Yu. I. Petunin, E. M. Semenov, Interpolation of Linear Operators, AMS, Prnvirlrnrf 1982, [extensions of Marcinkiewicz’ theorem, pp. 129-130,132-133 and 350; Maicinkiewicz spaces, pp, 112-118 and 117-130].
• [24] K.-S. Lau, On the Banach spaces of functions with bounded upper means, Pacific J. Math. 91 (1980), no. 1, 153-172.
• [25] K.-S. Lau, Extension of Wiener’s Tauberian identity and multipliers on the Marcinkiewicz space, Trans. Amer. Math. Soc. 277 (1983), no. 2, 489-506.
• [26] B.M. Levitan, Almost-Periodic Functions, Gosudarstv. Izdat. Tehn.-Teor. Lit., Moscow 1953, [Marcinkiewicz theorem, pp. 249-252].
• [27] J. Lindenstrauss, L. Tzafriri, Classical Banach Spaces, II. Function Spaces, Springer-Verlag, Berlin-New York 1979, [Marcinkiewicz interpolation theorem, pp. 149-150].
• [28] L. Maligranda, A generalization of the Shimogaki theorem, Studia Math. 71 (1981), no. 1, 69-83.
• [29] L. Maligranda, Indices and interpolation 234 (1985), 1-54, [Chapter 6, Part B, Marcinkiewicz interpolation theorem in Orlicz spaces].
• [30] L. Maligranda, On interpolation of nonlinear operators, Comment. Math. Prace Mat. 28 (1989), no. 2, 253-275.
• [31] L. Maligranda, Józef Marcinkiewicz (1910-1940) - on the centenary of his birth, Banach Center Publ. 95 (2011), 133-234.
• [32] J. Marcinkiewicz, Une remarque sur les espaces de M. Besicovitch, C. R. Acad. Sci. Paris 208 (1939), 157-159, reprinted in: Józef Marcinkiewicz, Collected Papers (A. Zygmund, ed.), PWN, Warsaw 1964, 470-472.
• [33] J. Marcinkiewicz, Sur I’interpolation d’operations, C. R. Acad. Sci. Paris 208 (1939), 1272-1273, reprinted in: Józef Marcinkiewicz, Collected Papers (A. Zygmund, ed.), PWN, Warsaw 1964, 539-540.
• [34] P. Nalli, Sopra una nuova specie di convergenza in media, Rend. Circ. Mat. Palermo (1)38 (1914), 305- 319 and 320-323.
• [35] E.T. Oklander, Interpolación, espacios de Lorentz y teorema de Murcinkicwics, Cursos y Seminarios de Matematica, vol. Fasc. 20, Universidad de Buenos Aires, Buenos Aires 1965.
• [36] J. Peetre,-On the development of interpolation-instead of a history three letters, in: Function Spaces, Interpolation Theory and Related Topics. Proc. of the International Conference in honour of Jaak Peetre on his 65th birthday (held at Lund University, Lund, Aug. 17-22, 2000) (M. Cwikel, M. Englis, A. Kufner, L.-E. Persson, G. Sparr, eds.), Walter de Gruyter, Berlin 2002, 39-48.
• [37] A. Pietsch, History ofBanach Spaces and Linear Operators, Birkhauser, Boston 2007, [The Marcinkiewicz interpolation theorem (1939), p. 433].
• [38] M. M. Rao, Z.D. Ren, Theory of Orlicz Spaces, Marcel Dekker, New York 1991, [Marcinkiewicz’s interpolation theorem for certain Orlicz spaces, Theorem 13, pp. 247-252].
• [39] M. Reed, B. Simon, Methods of Modern Mathematical Physics, II. Fourier Analysis, Self-Adjointness, Academic Press, New York-London 1975, [IX. 18 (Marcinkiewicz interpolation theorem)].
• [40] N. M. Riviere, Interpolation a la Marcinkiewicz, Rev. Un. Mat. Argentina 25 (1970/71), 363-377.
• [41] W.L. C. Sargent, Some analogues and extensions of Marcinkiewicz’s interpolation theorem, Proc. London Math. Soc. 1 (1961), 457-468.
• [42] E. M. Stein, G. Weiss, An extension of a theorem of Marcinkiewicz and some of its applications, J. Math. Mech. 8 (1959), 263-284.
• [43] E. M. Stein, G. Weiss, Introduction to Fourier Analysis on Euclidean Spaces, Princeton University Press, Princeton 1971, [Marcinkiewicz interpolation theorem, pp. 183-200].
• [44] R. S. Strichartz, A multilinear version of the Marcinkiewicz interpolation theorem, Proc. Amer. Math. Soc. 21 (1969), 441-444.
• [45] A. Torchinsky, Interpolation of operations and Orlicz classes, Studia Math. 59 (1976), no. 2, 177-207.
• [46] A. Torchinsky, Real-Variable Methods in Harmonic Analysis, Academic Press, Orlando 1986, [Marcinkiewicz interpolation theorem, pp. 86-91].
• [47] K. Urbanik, Fourier analysis in Marcinkiewicz spaces, Studia Math. 21 (1961), 93-102.
• [48] A. Zygmund, On a theorem of Marcinkiewicz concerning interpolation of operations, J. Math. Pures Appl. 35 (1956), 223-248.
• [49] A. Zygmund, Trigonometric Series, Vol. I, IL, Cambridge Univ. Press, Cambridge 1959, [Marcinkiewicz’s theorem on the interpolation of operators, pp. 111-120].
• [50] A. Zygmund, Józef Marcinkiewicz, in: Józef Marcinkiewicz, Collected Fdjju j (A, Zygmund, ed.), PWN, Warszawa 1964, 1-33.