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Grand Lorentz sequence space and its multiplication operator

Year 2020, , 771 - 781, 30.06.2020
https://doi.org/10.31801/cfsuasmas.680388

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}.

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, , 771 - 781, 30.06.2020
https://doi.org/10.31801/cfsuasmas.680388

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

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.

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

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