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Dichotomies for Orlicz spaces

  • Filip Strobin
Veröffentlicht/Copyright: 2. Mai 2016
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Mathematica Slovaca
Aus der Zeitschrift Mathematica Slovaca Band 66 Heft 1

Abstract

Assume that Lψ, Lψ1, …, Lψn are Orlicz spaces. We consider the size of the set Eψ(ψ1,…,ψn)={(f1,…,fn)∈Lψ1×…×Lψn: f1⋯fn∈Lψ}. We show that either it is very small (meager or σ-porous), or it is equal to Lψ1 × … × Lψn.

This work is a continuation of our previous papers, where we considered a similar problem for Lp spaces and Lorentz spaces.

Keywords: Orlicz spaces; multiplication; Baire category; porosity
MSC: Primary 46E30; 54E52; Secondary 46G99

This work has been supported by the Polish Ministry of Science and Higher Education Grant No. N N201 528 738.

  1. This paper has been communicated by Gregor Dolinar

Acknowledgement

We would like to thank the referees for a careful reading of the paper.

References

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Received: 2012-11-29
Accepted: 2013-6-28
Published Online: 2016-5-2
Published in Print: 2016-2-1

© 2016 Mathematical Institute Slovak Academy of Sciences

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https://doi.org/10.1515/ms-2015-0132
Schlagwörter für diesen Artikel
Orlicz spaces; multiplication; Baire category; porosity

Artikel in diesem Heft

  1. Research Article
  2. Prof. RNDr. Ján Jakubík, DrSc. passed away
  3. Research Article
  4. On the number of slim, semimodular lattices
  5. Research Article
  6. Quantum computational algebra with a non-commutative generalization
  7. Research Article
  8. Lexico groups and direct products of lattice ordered groups
  9. Research Article
  10. Values of limit periodic sequences and functions
  11. Research Article
  12. On representation of quasi-Hopf group coalgebras
  13. Research Article
  14. On the q-Bernstein polynomials of the logarithmic function in the case q > 1
  15. Research Article
  16. On some modification of Darboux property
  17. Research Article
  18. Separating sets by peripherally continuous functions
  19. Research Article
  20. Persistence and extinction of a stochastic delay predator-prey model in a polluted environment
  21. Research Article
  22. On O’Malley preponderantly continuous functions
  23. Research Article
  24. Inequalities for the normalized Jensen functional with applications
  25. Research Article
  26. Majorization of starlike and convex functions of complex order involving linear operators
  27. Research Article
  28. Fekete–Szegö problem for some starlike functions related to shell-like curves
  29. Research Article
  30. Central functions for classes of concave univalent functions
  31. Research Article
  32. Inclusion properties for classes of analytic functions associated with conic domains
  33. Research Article
  34. Uniqueness of meromorphic functions and nonlinear differential polynomials sharing a nonzero polynomial
  35. Research Article
  36. Solutions and constrained null-controllability for a differential-difference equation
  37. Research Article
  38. Oscillation criteria for quasi-linear neutral delay dynamic equations on time scale
  39. Research Article
  40. Time periodic solutions for a sixth order nonlinear parabolic equation
  41. Research Article
  42. Some inequalities of trigonometric approximation in weighted Orlicz spaces
  43. Research Article
  44. Summation methods applied to Voronovskaya-type theorems for the partial sums of Fourier series and for Fejér operators
  45. Research Article
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  47. Research Article
  48. On freely generated semigraph C*-algebras
  49. Research Article
  50. Operators with a given part of the numerical range
  51. Research Article
  52. Characterization of quasi-continuity of multifunctions of two variables
  53. Research Paper
  54. Confidence regions in singular weakly nonlinear regression models with constraints
  55. Research Article
  56. Global stability of an SEI model for plant diseases
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