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Year 2019, Volume: 48 Issue: 3, 771 - 778, 15.06.2019

Abstract

References

  • Y.A. Abramovich and C.D. Aliprantis, An invitation to operator theory, Graduate Studies in Mathematics, 50, American Mathematical Society, Providence, RI, 2002.
  • S.C. Arora, G. Datt, and S. Verma, Multiplication operators on Lorentz spaces, Indian J. Math. 48 (3), 317-329, 2006.
  • F.R. Astudillo-Villalba and J.C. Ramos-Fernández, Multiplication operators on the space of functions of bounded variation, Demonstr. Math. 50 (1), 105-115, 2017.
  • A. Benedek and R. Panzone, The spaces $L^P$, with mixed norm, Duke Math. J. 28, 301-324, 1961.
  • A.P. Blozinski, Multivariate rearrangements and Banach function spaces with mixed norms, Trans. Amer. Math. Soc. 263 (1), 149-167, 1981.
  • R.E. Castillo, H.C. Chaparro, and J.C. Ramos Fernández, Orlicz-Lorentz spaces and their multiplication operators, Hacet. J. Math. Stat. 44 (5), 991-1009, 2015.
  • R.E. Castillo, J.C. Ramos Fernández, and H. Rafeiro, Multiplication operators in variable Lebesgue spaces, Rev. Colombiana Mat. 49 (2), 293-305, 2015.
  • R.E. Castillo, J.C. Ramos Fernández and M. Salas-Brown, The essential norm of multiplication operators on Lorentz sequence spaces, Real Anal. Exchange 41 (1), 245-251, 2016.
  • R.E. Castillo, F.A. Vallejo Narváez and J.C. Ramos Fernández, Multiplication and composition operators on weak $L_p$ spaces, Bull. Malays. Math. Sci. Soc. 38 (3), 927- 973, 2015.
  • H.C. Chaparro, On Multipliers between Bounded Variation Spaces, Ann. Funct. Anal. 9 (3), 376-383, 2018.
  • W. Grey and G. Sinnamon, The inclusion problem for mixed norm spaces, Trans. Amer. Math. Soc. 368 (12), 8715-8736, 2016.
  • P.R. Halmos, What does the spectral theorem say?, Amer. Math. Monthly 70, 241-247, 1963.
  • H. Hudzik, R. Kumar and R. Kumar, Matrix multiplication operators on Banach function spaces, Proc. Indian Acad. Sci. Math. Sci. 116 (1), 71-81, 2006.
  • V. Kolyada and J. Soria, Mixed norms and iterated rearrangements, Z. Anal. Anwend. 35 (2), 119-138, 2016.
  • M. Mursaleen, A. Aghajani and K. Raj, Multiplication operators on Cesàro function spaces, Filomat 30 (5), 1175-1184, 2016.
  • J.C. Ramos-Fernández, Some properties of multiplication operators acting on Banach spaces of measurable functions, Bol. Mat. 23 (2), 221-237, 2016.
  • J.C. Ramos-Fernández and M. Salas-Brown, On multiplication operators acting on Köthe sequence spaces Afr. Mat. 28 (3-4), 661-667, 2017.
  • H. Takagi and K. Yokouchi, Multiplication and composition operators between two $L^p$-spaces, Function spaces (Edwardsville, IL, 1998), Contemp. Math. 232, Amer. Math. Soc., Providence, RI, 1999, 321-338.

Multiplication operators between mixed norm Lebesgue spaces

Year 2019, Volume: 48 Issue: 3, 771 - 778, 15.06.2019

Abstract

The boundedness, compactness and closed range of the multiplication operator defined on mixed norm Lebesgue spaces are characterized in this paper.

References

  • Y.A. Abramovich and C.D. Aliprantis, An invitation to operator theory, Graduate Studies in Mathematics, 50, American Mathematical Society, Providence, RI, 2002.
  • S.C. Arora, G. Datt, and S. Verma, Multiplication operators on Lorentz spaces, Indian J. Math. 48 (3), 317-329, 2006.
  • F.R. Astudillo-Villalba and J.C. Ramos-Fernández, Multiplication operators on the space of functions of bounded variation, Demonstr. Math. 50 (1), 105-115, 2017.
  • A. Benedek and R. Panzone, The spaces $L^P$, with mixed norm, Duke Math. J. 28, 301-324, 1961.
  • A.P. Blozinski, Multivariate rearrangements and Banach function spaces with mixed norms, Trans. Amer. Math. Soc. 263 (1), 149-167, 1981.
  • R.E. Castillo, H.C. Chaparro, and J.C. Ramos Fernández, Orlicz-Lorentz spaces and their multiplication operators, Hacet. J. Math. Stat. 44 (5), 991-1009, 2015.
  • R.E. Castillo, J.C. Ramos Fernández, and H. Rafeiro, Multiplication operators in variable Lebesgue spaces, Rev. Colombiana Mat. 49 (2), 293-305, 2015.
  • R.E. Castillo, J.C. Ramos Fernández and M. Salas-Brown, The essential norm of multiplication operators on Lorentz sequence spaces, Real Anal. Exchange 41 (1), 245-251, 2016.
  • R.E. Castillo, F.A. Vallejo Narváez and J.C. Ramos Fernández, Multiplication and composition operators on weak $L_p$ spaces, Bull. Malays. Math. Sci. Soc. 38 (3), 927- 973, 2015.
  • H.C. Chaparro, On Multipliers between Bounded Variation Spaces, Ann. Funct. Anal. 9 (3), 376-383, 2018.
  • W. Grey and G. Sinnamon, The inclusion problem for mixed norm spaces, Trans. Amer. Math. Soc. 368 (12), 8715-8736, 2016.
  • P.R. Halmos, What does the spectral theorem say?, Amer. Math. Monthly 70, 241-247, 1963.
  • H. Hudzik, R. Kumar and R. Kumar, Matrix multiplication operators on Banach function spaces, Proc. Indian Acad. Sci. Math. Sci. 116 (1), 71-81, 2006.
  • V. Kolyada and J. Soria, Mixed norms and iterated rearrangements, Z. Anal. Anwend. 35 (2), 119-138, 2016.
  • M. Mursaleen, A. Aghajani and K. Raj, Multiplication operators on Cesàro function spaces, Filomat 30 (5), 1175-1184, 2016.
  • J.C. Ramos-Fernández, Some properties of multiplication operators acting on Banach spaces of measurable functions, Bol. Mat. 23 (2), 221-237, 2016.
  • J.C. Ramos-Fernández and M. Salas-Brown, On multiplication operators acting on Köthe sequence spaces Afr. Mat. 28 (3-4), 661-667, 2017.
  • H. Takagi and K. Yokouchi, Multiplication and composition operators between two $L^p$-spaces, Function spaces (Edwardsville, IL, 1998), Contemp. Math. 232, Amer. Math. Soc., Providence, RI, 1999, 321-338.
There are 18 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Mathematics
Authors

Héctor Camilo Chaparro This is me 0000-0002-0723-8199

Publication Date June 15, 2019
Published in Issue Year 2019 Volume: 48 Issue: 3

Cite

APA Chaparro, H. C. (2019). Multiplication operators between mixed norm Lebesgue spaces. Hacettepe Journal of Mathematics and Statistics, 48(3), 771-778.
AMA Chaparro HC. Multiplication operators between mixed norm Lebesgue spaces. Hacettepe Journal of Mathematics and Statistics. June 2019;48(3):771-778.
Chicago Chaparro, Héctor Camilo. “Multiplication Operators Between Mixed Norm Lebesgue Spaces”. Hacettepe Journal of Mathematics and Statistics 48, no. 3 (June 2019): 771-78.
EndNote Chaparro HC (June 1, 2019) Multiplication operators between mixed norm Lebesgue spaces. Hacettepe Journal of Mathematics and Statistics 48 3 771–778.
IEEE H. C. Chaparro, “Multiplication operators between mixed norm Lebesgue spaces”, Hacettepe Journal of Mathematics and Statistics, vol. 48, no. 3, pp. 771–778, 2019.
ISNAD Chaparro, Héctor Camilo. “Multiplication Operators Between Mixed Norm Lebesgue Spaces”. Hacettepe Journal of Mathematics and Statistics 48/3 (June 2019), 771-778.
JAMA Chaparro HC. Multiplication operators between mixed norm Lebesgue spaces. Hacettepe Journal of Mathematics and Statistics. 2019;48:771–778.
MLA Chaparro, Héctor Camilo. “Multiplication Operators Between Mixed Norm Lebesgue Spaces”. Hacettepe Journal of Mathematics and Statistics, vol. 48, no. 3, 2019, pp. 771-8.
Vancouver Chaparro HC. Multiplication operators between mixed norm Lebesgue spaces. Hacettepe Journal of Mathematics and Statistics. 2019;48(3):771-8.