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Grand Lorentz sequence space and its multiplication operator

Year 2020, Volume: 69 Issue: 1, 771 - 781, 30.06.2020

Oğuz Oğur

https://doi.org/10.31801/cfsuasmas.680388
Cited By: 4

Abstract

In this paper, we introduce the grand Lorentz sequence spaces ℓ_{p,q)}^{θ} and study on some topological properties. Also, we characterize some properties of the multiplication operator, such as compactness, Fredholmness etc., defined on ℓ_{p,q)}^{θ}.

Keywords

Grand Lorentz sequence spaces multiplication operator compactness Fredholm operator

References

  • Altshuler, Z., Uniform convexity in Lorentz sequence spaces, Isr. J. Math., 20, (1975), 3-4.
  • Arora, S.C., Datt, G. and Verma, S., Operators on Lorentz sequence spaces, Math. Bohem., No:1, (2009), 87-98.
  • Bennett, C. and Sharpley, R., Interpolation Operators, Academic Press Inc. Toronto, 1988.
  • Corless, R. M., Gonnet, G. H., Hare, D. E. G., Jeffrey, D. J. and Knuth, E., On the Lambert W function, Adv. Comput. Math., 5(4), (1996), 329-359.
  • Crowe, J. A., Zweibel, J. A and Rosenbloom, P. C., Rearrangement of functions, J. Funct. Anal., 66, (1986), 432-438.
  • Hardy, G. H., Littlewood, J. E. and Polya, G., Inequalities, Cambridge Univ. Press, 1967.
  • Hunt, R. A., On L(p,q) spaces, Enseign. Math., 12, (1966), 249-276.
  • Iwaniec, T. and Sbordone, C., On the integrability of the Jacobian under minimal hypotheses, Arch. Ration. Mech. Anal., 119(2), (1992), 129-143.
  • Jain, P. and Kumari, S., On grand Lorentz spaces and the maximal operator, Math. Student, 79, 2010.
  • Kaminska, A. and Raynaud, Y., Isomorphic l_{p}-subspaces in Orlicz-Lorentz sequence spaces, Proc. Amer. Math. Soc., 134, (2006), 2317-2327.
  • Kato, M., On Lorentz spaces, Hiroshima Math. J., 6, (1976), 73-93.
  • Lorentz, G. G., Some new functional spaces, Ann. of Math, 2(51), (1950), 37-55.
  • Lorentz, G. G., On the theory of spaces Λ, Pacific J. Math., 1, (1951), 411-429.
  • Miyazaki, K., (p,q)-nuclear and (p,q)-integral operators, Hiroshima Math. J., 4, (1974), 99-132.
  • Oğur, O. and Duyar, C., On generalized Lorentz sequence space defined by modulus functions, Filomat, 30(2), (2016), 497-504.
  • Rafeiro, H., Samko, S. and Umarkhadzhiev, S., Grand Lebesgue sequence spaces, Georgian Math. J., 19(2), (2018), 235-246.
  • Samko, S. and Umarkhadzhiev, S., On grand Lebesgue spaces on sets of infinite measure, Math. Nachr., 290, (2017), 913-919.

Year 2020, Volume: 69 Issue: 1, 771 - 781, 30.06.2020

Oğuz Oğur

https://doi.org/10.31801/cfsuasmas.680388
Cited By: 4

Abstract

References

  • Altshuler, Z., Uniform convexity in Lorentz sequence spaces, Isr. J. Math., 20, (1975), 3-4.
  • Arora, S.C., Datt, G. and Verma, S., Operators on Lorentz sequence spaces, Math. Bohem., No:1, (2009), 87-98.
  • Bennett, C. and Sharpley, R., Interpolation Operators, Academic Press Inc. Toronto, 1988.
  • Corless, R. M., Gonnet, G. H., Hare, D. E. G., Jeffrey, D. J. and Knuth, E., On the Lambert W function, Adv. Comput. Math., 5(4), (1996), 329-359.
  • Crowe, J. A., Zweibel, J. A and Rosenbloom, P. C., Rearrangement of functions, J. Funct. Anal., 66, (1986), 432-438.
  • Hardy, G. H., Littlewood, J. E. and Polya, G., Inequalities, Cambridge Univ. Press, 1967.
  • Hunt, R. A., On L(p,q) spaces, Enseign. Math., 12, (1966), 249-276.
  • Iwaniec, T. and Sbordone, C., On the integrability of the Jacobian under minimal hypotheses, Arch. Ration. Mech. Anal., 119(2), (1992), 129-143.
  • Jain, P. and Kumari, S., On grand Lorentz spaces and the maximal operator, Math. Student, 79, 2010.
  • Kaminska, A. and Raynaud, Y., Isomorphic l_{p}-subspaces in Orlicz-Lorentz sequence spaces, Proc. Amer. Math. Soc., 134, (2006), 2317-2327.
  • Kato, M., On Lorentz spaces, Hiroshima Math. J., 6, (1976), 73-93.
  • Lorentz, G. G., Some new functional spaces, Ann. of Math, 2(51), (1950), 37-55.
  • Lorentz, G. G., On the theory of spaces Λ, Pacific J. Math., 1, (1951), 411-429.
  • Miyazaki, K., (p,q)-nuclear and (p,q)-integral operators, Hiroshima Math. J., 4, (1974), 99-132.
  • Oğur, O. and Duyar, C., On generalized Lorentz sequence space defined by modulus functions, Filomat, 30(2), (2016), 497-504.
  • Rafeiro, H., Samko, S. and Umarkhadzhiev, S., Grand Lebesgue sequence spaces, Georgian Math. J., 19(2), (2018), 235-246.
  • Samko, S. and Umarkhadzhiev, S., On grand Lebesgue spaces on sets of infinite measure, Math. Nachr., 290, (2017), 913-919.
There are 17 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Articles
Authors

Oğuz Oğur 0000-0002-3206-5330

Publication Date June 30, 2020
Submission Date January 27, 2020
Acceptance Date February 18, 2020
Published in Issue Year 2020 Volume: 69 Issue: 1

Cite

APA Oğur, O. (2020). Grand Lorentz sequence space and its multiplication operator. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 69(1), 771-781. https://doi.org/10.31801/cfsuasmas.680388
AMA Oğur O. Grand Lorentz sequence space and its multiplication operator. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. June 2020;69(1):771-781. doi:10.31801/cfsuasmas.680388
Chicago Oğur, Oğuz. “Grand Lorentz Sequence Space and Its Multiplication Operator”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69, no. 1 (June 2020): 771-81. https://doi.org/10.31801/cfsuasmas.680388.
EndNote Oğur O (June 1, 2020) Grand Lorentz sequence space and its multiplication operator. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69 1 771–781.
IEEE O. Oğur, “Grand Lorentz sequence space and its multiplication operator”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 69, no. 1, pp. 771–781, 2020, doi: 10.31801/cfsuasmas.680388.
ISNAD Oğur, Oğuz. “Grand Lorentz Sequence Space and Its Multiplication Operator”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69/1 (June 2020), 771-781. https://doi.org/10.31801/cfsuasmas.680388.
JAMA Oğur O. Grand Lorentz sequence space and its multiplication operator. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2020;69:771–781.
MLA Oğur, Oğuz. “Grand Lorentz Sequence Space and Its Multiplication Operator”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 69, no. 1, 2020, pp. 771-8, doi:10.31801/cfsuasmas.680388.
Vancouver Oğur O. Grand Lorentz sequence space and its multiplication operator. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2020;69(1):771-8.

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Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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