Denseness of the Lizorkin Space in Grand Lebesgue Spaces

For citation: Umarkhadzhiev S. M. Denseness of the Lizorkin Space in Grand Lebesgue Spaces. Vladikavkazskii matematicheskii zhurnal [Vladikavkaz Math. J.], vol. 17, no. 3, pp.75-83. DOI 10.23671/VNC.2017.3.7267

1. Umarhadzhiev S. M. Boundedness of linear operators in weighted
generalized grand lebesgue spaces. Vestn. AN Chechenskoj Respubliki
[Bulletin of the Academy of Sciences of the Chechen Republic], 2013,
vol. 2, no. 19, pp. 5-9 (Russian).

2. Umarhadzhiev S. M. Generalization of the notion of grand Lebesgue
space. Russian Mathematics [Izv. Vyssh. Uchebn. Zaved. Mat., 2014,
no. 4, pp. 42-51], 2014, vol. 58, no. 4, pp. 35-43.

3. Umarhadzhiev S. M. Boundedness of the Riesz potential operator in
weighted grand Lebesgue spaces. Vladikavkaz. Mat. Zh. [Vladikavkaz.
Math. J.], 2014, vol. 16, no. 2, pp. 62-68 (Russian).

4. Samko S.  G. Gipersinguljarnye Integraly i Ih Prilozhenija,
Rostov n/D., Izd-vo RGU, 1984, 208 p. (Russian).

5. Di Fratta G., Fiorenza A. A direct approach to the duality of
grand and small Lebesgue spaces. Nonlinear Analysis: Theory, Methods
and Applications, 2009, vol. 70, no. 7, pp. 2582-2592.

6. Fiorenza A. Duality and reflexivity in grand Lebesgue spaces.
Collect. Math., 2000, vol. 51, no. 2, pp. 131-148.

7. Fiorenza A., Gupta B., and Jain P. The maximal theorem in
weighted grand Lebesgue spaces. Stud. Math., 2008, vol. 188, no. 2,
pp. 123-133.

8. Fiorenza A. and Karadzhov G. E. Grand and small Lebesgue spaces
and their analogs. J. Anal. and its Appl., 2004, vol. 23, no. 4, pp.
657-681.

9. Fiorenza A. and  Rakotoson J. M. Petits espaces de Lebesgue et
leurs applications. C. R. Acad. Sci. Paris Ser. I, 2001, vol. 333,
pp. 1-4.

10. Greco L., Iwaniec T., and Sbordone C. Inverting the p-harmonic
operator. Manuscripta Math., 1997, vol. 92, pp. 249-258.

11. Iwaniec T. and Sbordone C. On the integrability of the Jacobian
under minimal hypotheses. Arch. Rational Mech. Anal., 1992, vol.
119, pp. 129-143.

12. Kokilashvili V. Weighted problems for operators of harmonic
analysis in some Banach function spaces. Lecture course of Summer
School and Workshop «Harmonic Analysis and Related Topics»
({HART}2010): Lisbon; [cited 2010 June 21-25], URL:
http://www.math.ist.utl.pt/\hart2010/kokilashvili.pdf.

13. Kokilashvili V. Boundedness criterion for the Cauchy singular
integraloperator in weighted grand Lebesgue spaces and application
to the Riemannproblem. Proc. A. Razmadze Math. Inst., 2009, vol.
151, pp. 129-133.

14. Kokilashvili V. The Riemann boundary value problem for analytic
functions in the frame ofgrand L^(p) spaces. Bull. Georgian Nat.
Acad. Sci., 2010, vol. 4, no. 1, pp. 5-7.

15. Kokilashvili V. and Meskhi A. A note on the boundedness of the
Hilberttransform in weighted grand Lebesgue spaces. Georgian Math.
J., 2009, vol. 16, no. 3, pp. 547-551.

16. Samko S. G. Hypersingular Integrals and their Applications,
London-N.Y., Taylor & Francis, 2002, xvii+358 p. (Ser. Analytical
Methods and Special Functions; vol. 5).

17. Samko S. G. and Umarkhadzhiev S. M. On Iwaniec - Sbordone spaces
on sets which may have infinite measure. Azerb. J. Math., 2011, vol.
1, no. 1, pp. 67-84.

18. Samko S. G. and Umarkhadzhiev S. M. On Iwaniec - Sbordone spaces
on sets which may have infinite measure: addendum. Azerb. J. Math.,
2011, vol. 1, no. 2, pp. 143-144.

19. Umarkhadzhiev S. M. The boundedness of the Riesz potential
operator from generalized grand Lebesgue spaces to generalized grand
Morrey spaces. Operator Theory: Advances and Applications,
Birkhauser, Basel, 2014, vol. 242, pp. 363-373.

20. Umarkhadzhiev S. M. A generalization concept of grand Lebesgue
space. Russian Math. (Izv. VUZ), 2014, vol. 58, no. 4, pp. 35-43.