Polynomial asymptotics and approximation of Sobolev functions
Hajłasz, Piotr ; Kałamajska, Agnieszka
Studia Mathematica, Tome 113 (1995), p. 55-64 / Harvested from The Polish Digital Mathematics Library

We prove several results concerning density of C0, behaviour at infinity and integral representations for elements of the space Lm,p=|mLp.

Publié le : 1995-01-01
EUDML-ID : urn:eudml:doc:216159
@article{bwmeta1.element.bwnjournal-article-smv113i1p55bwm,
     author = {Piotr Haj\l asz and Agnieszka Ka\l amajska},
     title = {Polynomial asymptotics and approximation of Sobolev functions},
     journal = {Studia Mathematica},
     volume = {113},
     year = {1995},
     pages = {55-64},
     zbl = {0823.46036},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv113i1p55bwm}
}
Hajłasz, Piotr; Kałamajska, Agnieszka. Polynomial asymptotics and approximation of Sobolev functions. Studia Mathematica, Tome 113 (1995) pp. 55-64. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv113i1p55bwm/

[00000] [1] H. Aikawa, On weighted Beppo Levi functions-integral representations and behavior at infinity, Analysis 9 (1989), 323-346. | Zbl 0697.31004

[00001] [2] O. V. Besov, The behaviour of differentiable functions at infinity and density of C0 functions, Trudy Mat. Inst. Steklov. 105 (1969), 3-14 (in Russian).

[00002] [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).

[00003] [4] J. Deny and J.-L. Lions, Les espaces du type de Beppo Levi, Ann. Inst. Fourier (Grenoble) 5 (1953-1954), 305-370. | Zbl 0065.09903

[00004] [5] T. Iwaniec and G. Martin, Quasiregular mappings in even dimensions, Acta Math. 170 (1993), 29-81. | Zbl 0785.30008

[00005] [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). | Zbl 0417.46041

[00006] [7] V. M. Maz'ya, Sobolev Spaces, Springer, 1985.

[00007] [8] Y. Mizuta, Integral representations of Beppo Levi functions of higher order, Hiroshima Math. J. 4 (1974), 375-396. | Zbl 0287.31005

[00008] [9] O. Nikodym, Sur une classe de fonctions considérées dans le problème de Dirichlet, Fund. Math. 21 (1933), 129-150. | Zbl 0008.15903

[00009] [10] L. Nirenberg, On elliptic partial differential equations, Ann. Scuola Norm. Sup. Pisa 13 (1959), 115-162. | Zbl 0088.07601

[00010] [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).

[00011] [12] K. T. Smith, Formulas to represent functions by their derivatives, Math. Ann. 188 (1970), 53-77. | Zbl 0187.03102

[00012] [13] S. L. Sobolev, The density of C0 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.

[00013] [14] S. L. Sobolev, The density of C0 finite functions in the L(m)p space, Sibirsk. Mat. Zh. 4 (1963), 673-682 (in Russian). | Zbl 0204.43802

[00014] [15] E. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Univ. Press, 1970. | Zbl 0207.13501