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2002 | [Z] 42(1) | 37-51
Tytuł artykułu

On constants in the pointwise one-dimensional multiplicative inequalities

Autorzy
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We give the bounds on constants in the one-dimensional pointwise multiplicative inequalities [formula] where Mf(x) is the Hardy-Littlewood maximal function of f. Our constants are optimal in the case k=1, m=2.
Słowa kluczowe
Wydawca

Rocznik
Tom
Strony
37-51
Opis fizyczny
Bibliogr. 24 poz., tab.
Twórcy
  • Institute of Mathematics, Warsaw University, ul. Banacha 2, 02-097 Warszawa, Polska, kalamajs@mimuw.edu.pl
Bibliografia
  • [1] V. V. Arestov, Some extremal problems for differentiable functions in of variable, Trudy Mat. Inst. Steklov. 138 (1975), 3-28 (in Russian).
  • [2] D. R. Adams, L. I. Hedberg, Function Spaces and Potential Theory, Springer-Verlag, Berlin 1996.
  • [3] V. Burenkov, Sobolev Spaces on Domains, B. G. Taubner, Stuttgart-Leipzig, 1998.
  • [4] V. Burenkov, On sharp constants in the inequalities for the norms of intermediate derivatives on finite interval, II, Trudy Mat. Inst. Steklov 173 (1986), 38-49 (in Russian), English transl. in Proc. Steklov Inst. Math. 173 (1986).
  • [5] L. C. Evans, Partial Differential Equations, Graduate Studies in Mathematics, vol. 19, AMS, Providence, 1998.
  • [6] E. Gagliardo, Ulteriori properieta di alcune classi di funzzioni in piau variabli, Riserche di Mat. Napoli 8 (1959), 24-51.
  • [7] V. N. Gabushin, Inequalities for norm of functions and their derivatives in LP metrics, Math. Zametki 3 (1967), 291-298 (in Russian).
  • [8] A. Kałamajska, Pointwise multiplicative inequalities and Nirenberg type estimates in weighted Sobolev spaces, Studia Math. 108 (1994), 275-290.
  • [9] A. Kałamajska, Coercive inequalities on weighted Sobolev spaces, Coll. Math. 66 (1994), 309-318.
  • [10] A. N. Kolmogorov, On inequalities between upper bounds of consecutive derivatives of an arbitrary function defined on an infinite interval, Uchen. Zap. MGY, Matematica, 30 No.3 (1939), 13-16.
  • [11] M. K. Kwong, A. Zettl, Norm inequalities for derivatives (Proc. Six’th Conf. Univ. Dundee, Dundee), Lect. Notes Math. 846, Springer (1981), 227-243.
  • [12] O. A. Ladyzenskaja, N. N. Uraltsewa, Linear and Quasilinear Equations of Elliptic Type, Nauka, Moscov, 1973 (in Russian).
  • [13] O. A. Ladyzenskaja, W. A. Solonnikov, N. N. Uraltsewa, Linear and Quasilinear Equations of Parabolic Type, Nauka, Moscov 1967 (in Russian).
  • [14] V. G. Maz’ya, Sobolev Spaces, Springer-Verlag 1985.
  • [15] V. G. Mazy’a, A. Kufner, Variations on the theme inequality (ƒ')2 ≤ 2ƒsup|ƒ"|, Manuscripta Math. 56 (1986), 89-104.
  • [16] V. G. Maz’ya, T. Shaposhnikova, On pointwise interpolation inequalities for derivatives, Math. Bohemica 124 (1999), 131-148.
  • [17] V. G. Maz’ya, T. Shaposhnikova, Pointwise Interpolation Inequalities for Riesz and Bessel Potentials, preprint LiTH-MAT-R-99-15.
  • [18] V. G. Maz’ya, T. Shaposhnikova, Maximal Banach Algebra in Spaces of Multipliers between Bessel Potential Spaces, preprint LiTH-MAT-R-99-16.
  • [19] V. G. Maz’ya, T. Shaposhnikova, Maximal Algebra of Multipliers Between Fractional Sobolev Spaces, preprint LiTH-MAT-R-2000-02.
  • [20] B. Muckenhoupt, Weighted norm inequalities for the Hardy maximal function, Trans. Amer. Math. Soc. 165 (1972), 207-227.
  • [21] V. G. Maz’ya, T. Shaposhnikova, Jacques Hadamard, a universal mathematician, American Mathematical Society and London Mathematical Society, Providence, RI, 1998.
  • [22] L. Nirenberg, On elliptic partial differential equations, Ann. Scuola Norm. Sup. di Pisa, 13, v. 3 (1959), 115-162.
  • [23] L. Nirenberg, An extended interpolation inequality, Ann. Scuola Norm. Sup. di Pisa 20, v. 4 (1966), 733-737.
  • [24] W. M. Tichomirov, Some Questions of Approximation Theory, MGU, 1976 (in Russian).
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.baztech-article-BUS2-0002-0045
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