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Indices and interpolation

Autorzy

Lech Maligranda

Seria

Rozprawy Matematyczne tom/nr w serii: 234 wydano: 1985

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Pełne teksty:
rm23401.pdf

Warianty tytułu

Abstrakty

EN

CONTENTS
0. Introduction.............................................................................5
1. Submultiplicative functions and indices...................................7
2. Indices of measurable functions...........................................12
3. Indices of Orlicz spaces........................................................19
4. Indices of rearrangement invariant spaces...........................25
5. Interpolation theorems for weak type operators....................29
6. Some additional remarks and open problems.......................39
 A. Indices of Lorentz-Orlicz spaces..........................................39
 B. Marcinkiewicz interpolation theorem in Orlicz spaces...........41
 C. Indices and strong interpolation..........................................43
 D. Indices and interpolation of compact operators...................45
References...............................................................................47

Słowa kluczowe

Tematy

Wydawca

Instytut Matematyczny Polskiej Akademii Nauk

Miejsce publikacji

Warszawa

Copyright

Seria

Rozprawy Matematyczne tom/nr w serii: 234

Liczba stron

49

Liczba rozdzia³ów

Opis fizyczny

Dissertationes Mathematicae, Tom CCXXXIV

Daty

wydano
1985

Twórcy

autor
Lech Maligranda

Bibliografia

  • [1] N. K. Bari and S. B. Stechkin, The best approximation and differential properties of two conjugate functions, Trudy Mosk. Mat. Obshch. 5 (1956), 483-522 (in Russian).
  • [2] C. Bennett, Banach function spaces and interpolation methods I. The abstract theory, J. Functional Analysis 17 (1974), 409-440.
  • [3] Z. W. Birnbaum and W. Orlicz, Über die Verallgemeinerung des Begriffes der zueinander konjugierten Potenzen, Studia Math. 3 (1931), 1-67.
  • [4] D. W. Boyd, The Hilbert transform on rearrangement invariant spaces, Canad. J. Math, 19 (1967), 599-616.
  • [5] D. W. Boyd, The spectral radius of averaging operators. Pacific J. Math. 24 (1968), 19-28.
  • [6] D. W. Boyd, Indices of function spaces and their relationship to interpolation, Canad. J. Math. 21 (1969), 1245-1254.
  • [7] D. W. Boyd, Monotone semigroups of operators on cones, Canad. Math. Bull. 12 (1969), 299-309.
  • [8] D. W. Boyd, Indices for the Orlicz spaces. Pacific J. Math. 38 (1971), 315-323.
  • [9] A. P. Calderon, Spaces between L¹ and $L^∞$ and the theorem of Marcinkiewicz, Studia Math. 26 (1966), 273-299.
  • [10] C. E. Cleaver, Packing spheres in Orlicz spaces. Pacific J. Math. 65 (1976), 325-335.
  • [11] R. Cooper, The converses of the Cauchy-Holder inequality and the solutions of the inequality g(x+y) ≤ g(x) + g(y), Proc. London Math. Soc. 26 (1927), 415-432.
  • [12] A. A. Dmitriev and E. M. Semenov, On operators of weak type (1,1), Sibirsk. Mat. Zh. 20 (1979), 656-658 (in Russian).
  • [13] D. Drasin and D. F. Shea, Pólya peaks and the oscillation of positive functions, Proc. Amer. Math. Soc. 34 (1972), 403-411.
  • [14] F. Féher, A note on weak-type interpolation and function spaces. Bull. London Math. Soc. 12 (1980), 443-451.
  • [15] C. M. Goldie, Convergence theorems for empirical Lorentz curves and their inverses. Adv. in Appl. Probab. 9 (1977), 765-791.
  • [16] J. Gustavsson and J. Peetre, Interpolation of Orlicz spaces, Studia Math. 60 (1977), 33-59.
  • [17] E. Hille and R. S. Phillips, Functional Analysis and Semi-Groups, Providence, 1957.
  • [18] W. B. Johnson, B. Maurey, G. Schechtman and L. Tzafriri, Symmetric Structures in Banach Spaces, Memoirs Amer. Math. Soc. 1979.
  • [19] N.J. Kalton, Orlicz sequence spaces without local convexity, Math. Proc. Camb. Phil. Soc. 81 (1977), 253-277.
  • [20] S. Koizumi, On the singular integrals I, Proc. Japan Acad. 34 (1958), 193-198.
  • [21] M. A. Krasnoselski and Ya. B. Ruticki, Convex functions and Orlicz spaces, P. Noordhoof, Groningen, 1961.
  • [22] S. G. Krein, Yu. I. Petunin and E. M. Semenov, Interpolation of Linear Operators, Nauka, Moscow 1978 (in Russian).
  • [23] S. G. Krein and E. M. Semenov, Interpolation of operators of weakened type, Funkctional. Anal. i Prilozhen 7 (1973), 89-90 (in Russian).
  • [24] R. Leśniewicz and W. Orlicz, On generalized variations II, Studia Math. 45 (1973), 71-109.
  • [25] K. J. Lindberg, On subspaces of Orlicz sequence spaces, Studia Math. 45 (1973), 119-146.
  • [26] J. Lindenstrauss and L. Tzafriri, On Orlicz sequence spaces III, Israel J. Math. 14 (1973), 368-389.
  • [27] J. Lindenstrauss and L. Tzafriri, Classical Banach spaces I. Sequence Spaces, Springer-Verlag, Berlin-Heidelberg-New York 1977.
  • [28] J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces II. Function Spaces, Springer-Verlag, Berlin-Heidelberg-New York 1979.
  • [29] G. G. Lorentz, On the theory of spaces Λ, Pacific J. Math. 1 (1951), 411-429.
  • [30] G. G. Lorentz and T. Shimogaki, Interpolation theorem for operators in function spaces, J. Functional Analysis 2 (1968), 31-51.
  • [31] G. G. Lorentz and T. Shimogaki, Majorants for interpolation theorems, Publ. Ramanujan Inst. 1 (1969), 115-122.
  • [32] G. G. Lorentz and T. Shimogaki, Interpolation theorems for the pairs of spaces $(L^p, L^∞)$ and $(L¹, L^q)$, Trans. Amer. Math. Soc. 159 (1971), 207-221.
  • [33] W. A.J. Luxemburg, Banach function spaces, Thesis, Delft Technical Univ. 1955.
  • [34] L. Maligranda, Interpolation of Lipschitz operators for the pairs of spaces $(L^p, L^∞)$, and $(l^p, C_0)$, 0 < p < ∞, Functiones et Approximatio 9 (1980), 107-115.
  • [35] L. Maligranda, A generalization of the Shimogaki theorem, Studia Math. 71 (1981), 69-83.
  • [36] L. Maligranda, Generalized Hardy inequalities in rearrangement invariant spaces, J. Math. Pures Appl. 59 (1980), 405-415.
  • [37] R. A. Mailer, Relative stability, characteristic functions and stochastic compactness, J. Austral. Math. Soc. Ser. A, 28 (1979), 499-509.
  • [38] W. Matuszewska, Some further properties of (p-functions, Bull. Acad. Polon. Sci., Sér. Sci. Math. Astronom. Phys. 9 (1961), 445-450.
  • [39] W. Matuszewska, Regularly increasing functions in connection with the theory of $L^{*φ}$-spaces, Studia Math. 21 (1962), 317-344.
  • [40] W. Matuszewska, On a generalization of regularly increasing functions, Studia Math. 24 (1964), 271-279.
  • [41] W. Matuszewska and W. Orlicz, On certain properties of φ-functions, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 8 (1960), 439-443.
  • [42] W. Matuszewska and W. Orlicz, On some classes of functions with regard to their orders of growth, Studia Math. 26 (1965), 11-24.
  • [43] S. Mazur and W. Orlicz, On some classes of linear spaces, Studia Math. 17 (1958), 97-119.
  • [44] B. Muckenhoupt, Hardy's inequality with weights, Studia Math. 44 (1972), 31-38.
  • [45] N.I. Nielsen, On the Orlicz Junction space $L_M(0,∞)$, Israel Jour. Math. 20 (1975), 237-259.
  • [46] A. M. Ostrowski, On Cauchy-Frullani integrals, Comment. Math. Helv. 51 (1976), 57-91.
  • [47] E. A. Pavlov, On the Calderdn type operator, Analysis Mathematica, 4 (1978), 117-124 (in Russian).
  • [48] L. A. Rubel, A pathological Lebesgue-measurable function. Jour. London Math. Soc. 38 (1963), 1-4.
  • [49] E. M. Semenov, A new interpolation theorem, Funkctional. Anal. i Prilozhen. 2 (1968), 158-168 (in Russian),
  • [50] E. Seneta, Regularly varying functions, Lecture Notes in Mathematics 508, Springer-Verlag, Berlin-Heidelberg-New York 1976.
  • [51] R. Sharpley, Spaces $Λ_α(X)$ and interpolation, J. Functional Analysis 11 (1972), 479-513.
  • [52] R. Sharpley, Interpolation theorems for compact operators, Indiana Univ. Math. J. 22 (1973), 965-984.
  • [53] R. Sharpley, Interpolation of n pairs and counterexamples employing indices, J. Approximation Theory 13 (1975), 117-127.
  • [54] T. Shimogaki, On the complete continuity of operators in an interpolation theorem. Jour. Fac. Sci. Hokkaido Univ. Ser. I. 20 (1968), 109-114.
  • [55] T. Shimogaki, A note on norms of compression operators on function spaces, Proc. Japan Acad. 46 (1970), 239-242.
  • [56] T. Shimogaki, Indices of function spaces (preprint).
  • [57] H. Silverman, Properties of Polya peaks. Rocky Mountain Math. J. 1 (1971), 649-656.
  • [58] I. B. Simonenko, Interpolation and extrapolation of linear operators in Orlicz spaces. Mat. Sb. 63 (1964), 536-553 (in Russian).
  • [59] G. Sparr, Interpolation of weighted $L_p$-spaces, Studia Math. 62 (1978), 229-271.
  • [60] A. Torchinsky, Interpolation of operations and Orlicz spaces, Studia Math. 59 (1976), 177-207.
  • [61] P. Turpin, Convexités dans les espaces vectoriels topologiques généraux, Diss. Math. 131 (1976).
  • [62] S. Yamamuro, Exponents of modulared semi-ordered linear spaces, J. Fac. Sci. Hokkaido Univ. 12 (1953), 211-253.
  • [63] S. Yamamuro, Modulared sequence spaces, Jour. Fac. Sci. Hokkaido Univ. Ser. I 13 (1954), 1-12
  • [64] M. Zippin, Interpolation of operators of weak type between rearrangement invariant spaces, J. Functional Analysis 7 (1971), 267-284.
  • [65] A. Zygmund, Trigonometric Series, Cambridge Univ. Press, Vol. I, II, 1959.
  • [66] N. H. Bingham and C. M. Goldie, Extensions of regular variation, I: Uniformity and quantifiers; II: Representations and indices, Proc. London Math. Soc. 44 (1982), 473-496, 497-534.
  • [67] V.I. Dmitriev and S. G. Krein, Interpolation of operators of weak type, Analysis Mathematica 4 (1978), 83-99.
  • [68] V. K. Dzjadyk, An introduction to the theory of uniformly approximation functions by polynomials, Nauka, Moscow 1977 (in Russian).
  • [69] F. Fehér, The Marcinkiewicz Interpolation Theorem for rearrangement-invariant function spaces and applications, Zeit. Anal. and ihre Anwend. 2 (1983), 111-125.
  • [70] L. Maligranda, On Hardy's inequality in weighted rearrangement invariant spaces and applications I, II, Proc. Amer. Math. Soc. 88 (1983), 67-74, 75-80.
  • [71] E. A. Pavlov, On Calderón's operator, Ukr. Mat. Žurnal 33 (1981), 142-143.
  • [72] Y. Sagher, Real interpolation with weights, Indiana Univ. Math. J. 30 (1981), 113-121.
  • [73] J. O. Strömberg, Bounded mean oscillation with Orlicz norms and duality of Hardy spaces, Indiana Univ. Math. J. 28 (1979), 511-544.

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bwmeta1.element.zamlynska-c6284b5e-9d18-4548-b714-caa39ff9d8fb

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ISBN
83-01-05818-B
ISSN
0012-3862

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DML-PL
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