Polynomial asymptotics and approximation of Sobolev functions

Piotr Hajłasz; Agnieszka Kałamajska

Studia Mathematica (1995)

  • Volume: 113, Issue: 1, page 55-64
  • ISSN: 0039-3223

Abstract

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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 .

How to cite

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Hajłasz, Piotr, and Kałamajska, Agnieszka. "Polynomial asymptotics and approximation of Sobolev functions." Studia Mathematica 113.1 (1995): 55-64. <http://eudml.org/doc/216159>.

@article{Hajłasz1995,
abstract = {We prove several results concerning density of $C_\{0\}^\{∞\}$, behaviour at infinity and integral representations for elements of the space $L^\{m,p\} = \{⨍ | ∇^\{m\}⨍ ∈ L^p\}$.},
author = {Hajłasz, Piotr, Kałamajska, Agnieszka},
journal = {Studia Mathematica},
keywords = {Sobolev space; Beppo Levi space; approximation; polynomial asymptotics; density of $C_0^∞$ functions; integral representations for elements of the space },
language = {eng},
number = {1},
pages = {55-64},
title = {Polynomial asymptotics and approximation of Sobolev functions},
url = {http://eudml.org/doc/216159},
volume = {113},
year = {1995},
}

TY - JOUR
AU - Hajłasz, Piotr
AU - Kałamajska, Agnieszka
TI - Polynomial asymptotics and approximation of Sobolev functions
JO - Studia Mathematica
PY - 1995
VL - 113
IS - 1
SP - 55
EP - 64
AB - We prove several results concerning density of $C_{0}^{∞}$, behaviour at infinity and integral representations for elements of the space $L^{m,p} = {⨍ | ∇^{m}⨍ ∈ L^p}$.
LA - eng
KW - Sobolev space; Beppo Levi space; approximation; polynomial asymptotics; density of $C_0^∞$ functions; integral representations for elements of the space
UR - http://eudml.org/doc/216159
ER -

References

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  1. [1] H. Aikawa, On weighted Beppo Levi functions-integral representations and behavior at infinity, Analysis 9 (1989), 323-346. Zbl0697.31004
  2. [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. [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. [4] J. Deny and J.-L. Lions, Les espaces du type de Beppo Levi, Ann. Inst. Fourier (Grenoble) 5 (1953-1954), 305-370. Zbl0065.09903
  5. [5] T. Iwaniec and G. Martin, Quasiregular mappings in even dimensions, Acta Math. 170 (1993), 29-81. Zbl0785.30008
  6. [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). Zbl0417.46041
  7. [7] V. M. Maz'ya, Sobolev Spaces, Springer, 1985. 
  8. [8] Y. Mizuta, Integral representations of Beppo Levi functions of higher order, Hiroshima Math. J. 4 (1974), 375-396. Zbl0287.31005
  9. [9] O. Nikodym, Sur une classe de fonctions considérées dans le problème de Dirichlet, Fund. Math. 21 (1933), 129-150. Zbl0008.15903
  10. [10] L. Nirenberg, On elliptic partial differential equations, Ann. Scuola Norm. Sup. Pisa 13 (1959), 115-162. Zbl0088.07601
  11. [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. [12] K. T. Smith, Formulas to represent functions by their derivatives, Math. Ann. 188 (1970), 53-77. Zbl0187.03102
  13. [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. [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). Zbl0204.43802
  15. [15] E. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Univ. Press, 1970. Zbl0207.13501

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