On spaces L p ( x ) and W k , p ( x )

Ondrej Kováčik; Jiří Rákosník

Czechoslovak Mathematical Journal (1991)

  • Volume: 41, Issue: 4, page 592-618
  • ISSN: 0011-4642

How to cite


Kováčik, Ondrej, and Rákosník, Jiří. "On spaces $L^{p(x)}$ and $W^{k, p(x)}$." Czechoslovak Mathematical Journal 41.4 (1991): 592-618. <http://eudml.org/doc/13956>.

author = {Kováčik, Ondrej, Rákosník, Jiří},
journal = {Czechoslovak Mathematical Journal},
keywords = {Lebesgue and Sobolev spaces with variable order of integrability; embedding theorems; Sobolev-type spaces; weak solution; nonlinear boundary value problem},
language = {eng},
number = {4},
pages = {592-618},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On spaces $L^\{p(x)\}$ and $W^\{k, p(x)\}$},
url = {http://eudml.org/doc/13956},
volume = {41},
year = {1991},

AU - Kováčik, Ondrej
AU - Rákosník, Jiří
TI - On spaces $L^{p(x)}$ and $W^{k, p(x)}$
JO - Czechoslovak Mathematical Journal
PY - 1991
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 41
IS - 4
SP - 592
EP - 618
LA - eng
KW - Lebesgue and Sobolev spaces with variable order of integrability; embedding theorems; Sobolev-type spaces; weak solution; nonlinear boundary value problem
UR - http://eudml.org/doc/13956
ER -


  1. F. E. Browder, Problémes non-linéaires, Seminaire de Mathématiques superieures. Montréal, 1966. (1966) Zbl0153.17302MR0250140
  2. H. Hudzik, The problems of separability, duality, reflexivity and of comparision for generalized Orlicz-SoboIev space W M k ( Ω ) , Comment. Math. 21 (1979), 315-324. (1979) MR0577521
  3. A. Kozek, Convex integral functionals on Orlicz spaces, Comment. Math. 21 (1980), 109-135. (1980) MR0577677
  4. M. A. Krasnoseľskii, Topological methods in the theory of nonlinear integral equations, (Russian) Gosudarstv. Izdat. Tehn.-Teor. Lit., Moscow, 1956. English transl.: Pergamon Press Book, The Macmillan Co., New York, 1964. (1956) MR0159197
  5. M. A. Krasnoseľskii, Ya. B. Rutickii, Convex functions and Orlicz spaces, (Russian) Gosudarstv. Izdat. Fiz.-Mat. Lit., Moscow. 1958. English transl.: P. Noordhoff, Groningen, 1961. (1958) MR0126722
  6. J.Musielak, Orlicz spaces and modular spaces, Springer-Verlag, Berlin, 1983. (1983) Zbl0557.46020MR0724434

Citations in EuDML Documents

  1. T. S. Kopaliani, On some structural properties of Banach function spaces and boundedness of certain integral operators
  2. Idrissa Ibrango, Stanislas Ouaro, Entropy solution for doubly nonlinear elliptic anisotropic problems with Fourier boundary conditions
  3. J. J. Manfredi, J. D. Rossi, J. M. Urbano, p x -harmonic functions with unbounded exponent in a subdomain
  4. Hans-Gerd Leopold, Embedding of function spaces of variable order of differentiation in function spaces of variable order of integration
  5. Michael Růžička, Modeling, mathematical and numerical analysis of electrorheological fluids
  6. Gerardo R. Chacón, Gerardo A. Chacón, Variable exponent Fock spaces
  7. Ghasem A. Afrouzi, Shaeid Shokooh, Nguyen T. Chung, Infinitely many weak solutions for a non-homogeneous Neumann problem in Orlicz--Sobolev spaces
  8. Jingshi Xu, The boundedness of multilinear commutators of singular integrals on Lebesgue spaces with variable exponent
  9. Mitsuo Izuki, Yoshihiro Sawano, Variable Lebesgue norm estimates for BMO functions
  10. Yongqiang Fu, Binlin Zhang, Weak solutions for elliptic systems with variable growth in Clifford analysis

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