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1995 | 113 | 1 | 55-64
Tytuł artykułu

Polynomial asymptotics and approximation of Sobolev functions

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EN
We prove several results concerning density of $C_{0}^{∞}$, behaviour at infinity and integral representations for elements of the space $L^{m,p} = {⨍ | ∇^{m}⨍ ∈ L^p}$.
Twórcy
  • Institute of Mathematics, Warsaw University, Banacha 2, 02-097 Warszawa, Poland, hajlasz@mimuw.edu.pl
Bibliografia
  • [1] H. Aikawa, On weighted Beppo Levi functions-integral representations and behavior at infinity, Analysis 9 (1989), 323-346.
  • [2] O. V. Besov, The behaviour of differentiable functions at infinity and density of $C^∞_0$ functions, Trudy Mat. Inst. Steklov. 105 (1969), 3-14 (in Russian).
  • [3] O. V. Besov, V. P. Il'in and S. M. Nikol'skiĭ, Integral Representations of Functions and Imbedding Theorems, Moscow, Nauka, 1975 (in Russian).
  • [4] J. Deny and J.-L. Lions, Les espaces du type de Beppo Levi, Ann. Inst. Fourier (Grenoble) 5 (1953-1954), 305-370.
  • [5] T. Iwaniec and G. Martin, Quasiregular mappings in even dimensions, Acta Math. 170 (1993), 29-81.
  • [6] P. I. Lizorkin, On the behaviour at infinity of functions from the Liouville class. On Riesz potentials of an arbitrary order, Trudy Mat. Inst. Steklov. 150 (1979), 174-197 (in Russian).
  • [7] V. M. Maz'ya, Sobolev Spaces, Springer, 1985.
  • [8] Y. Mizuta, Integral representations of Beppo Levi functions of higher order, Hiroshima Math. J. 4 (1974), 375-396.
  • [9] O. Nikodym, Sur une classe de fonctions considérées dans le problème de Dirichlet, Fund. Math. 21 (1933), 129-150.
  • [10] L. Nirenberg, On elliptic partial differential equations, Ann. Scuola Norm. Sup. Pisa 13 (1959), 115-162.
  • [11] V. N. Sedov, On functions tending to a polynomial at infinity, in: Imbedding Theorems and Their Applications (Proc. Sympos. Imbedding Theorems, Baku, 1966), Moscow, 1970, 204-212 (in Russian).
  • [12] K. T. Smith, Formulas to represent functions by their derivatives, Math. Ann. 188 (1970), 53-77.
  • [13] S. L. Sobolev, The density of $C^∞_0$ functions in the $L^(m)_p$ space, Dokl. Akad. Nauk SSSR 149 (1963), 40-43 (in Russian); English transl.: Soviet Math. Dokl. 4 (1963), 313-316.
  • [14] S. L. Sobolev, The density of $C^∞_0$ finite functions in the $L^(m)_p$ space, Sibirsk. Mat. Zh. 4 (1963), 673-682 (in Russian).
  • [15] E. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Univ. Press, 1970.
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Bibliografia
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bwmeta1.element.bwnjournal-article-smv113i1p55bwm
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