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Orlicz algebras associated to a Banach function space

Year 2024, Volume: 53 Issue: 1, 191 - 200, 29.02.2024
https://doi.org/10.15672/hujms.1018098

Abstract

In this paper, we study the spaces ${\mathcal X}^\Phi$ as Banach algebras, where $\mathcal X$ is a quasi-Banach function space and $\Phi$ is a Young function, and extend some well-known facts regarding Lebesgue and Orlicz spaces on this new structure. Also, for each $p\geq 1$, we give some necessary condition for the space $\mathcal{X}^p$ to be a Banach algebra under the pointwise product.

References

  • [1] A.R. Bagheri Salec and S.M. Tabatabaie, Some necessary and sufficient conditions for convolution weighted Orlicz algebras, Bull. Iranian Math. Soc. 48, 2509-2520, 2022.
  • [2] A.R. Bagheri Salec, S. Ivkovic and S.M. Tabatabaie, Spaceability on some classes of Banach spaces, Math. Ineq. Appl. 25(3), 659-672, 2022.
  • [3] A.R. Bagheri Salec, V. Kumar and S.M. Tabatabaie, Convolution properties of Orlicz spaces on hypergroups, Proc. Amer. Math. Soc. 150(4), 1685-1696, 2022.
  • [4] L. Bernal-González and M.O. Cabrera, Spaceability of strict order integrability, J. Math. Anal. Appl. 385, 303-309, 2012.
  • [5] R. del Campo, A. Fernández, F. Mayoral and F. Naranjo, Orlicz spaces associated to a quasi-Banach function space. Applications to vector measures and interpolation, Collect. Math. 72, 481-499, 2021.
  • [6] S. Glab and F. Strobin, Dichotomies for $L^p$ spaces, J. Math. Anal. Appl. 368, 382-390, 2010.
  • [7] S. Glab and F. Strobin, Spaceability of sets in $L^p\times L^q$ and $C_0\times C_0$, J. Math. Anal. Appl. 440, 451-465, 2016.
  • [8] H. Hudzik, Orlicz spaces of essentially bounded functions and Banach-Orlicz algebras, Arch. Math. 44, 535-538, 1985.
  • [9] H. Hudzik, A. Kamiska and J. Musielak, On some Banach algebras given by a modular, in: Alfred Haar Memorial Conference, Budapest, Colloquia Mathematica Societatis J anos Bolyai (North Holland, Amsterdam), 49, 445-463, 1985.
  • [10] P. Jain, L.E. Persson and P. Upreti, Inequalities and properties of some generalized Orlicz classes and spaces, Acta Math. Hungar. 117, 161-174, 2007.
  • [11] V. Kumar, R. Sarma and N. Shravan Kumar, Orlicz algebras on homogeneous spaces of compact groups and their abstract linear representations, Mediterr. J. Math. 15(4), 186, 2018.
  • [12] V. Kumar, R. Sarma and N. Shravan Kumar, Orlicz spaces on hypergroups, Publ. Math. Debrecen 94(1-2), 31-47, 2019.
  • [13] L. Maligranda and L.E. Persson, Generalized duality of some Banach function spaces, Proc. Konin. Nederlands Akad. Wet. 92, 323-338, 1989.
  • [14] S. Okada, W. Ricker, and E.A. Sánchez-Pérez, Optimal domain and integral extension of operators acting in functions spaces, Operator Theory: Advances and Applications, vol. 180, Birkhäuser, Verlag, Besel, 2008.
  • [15] A. Osançlıol and S. Öztop, Weighted Orlicz algebras on locally compact groups, J. Aust. Math. Soc. 99, 399-414, 2015.
  • [16] S. Öztop and S.M. Tabatabaie, Weighted Orlicz algebras on hypergroups, FILOMAT, 34(7), 2131-2139, 2020.
  • [17] L. E. Persson, Some elementary inequalities in connection with Xp-spaces, in: Constructive Theory of Functions, 367-376, 1988.
  • [18] L. E. Persson, On some generalized Orlicz classes and spaces, Research Report 1988-3, Department of Mathematics, Lulea University of Technology, 1988.
  • [19] T.S. Quek and L.Y.H. Yap, Sharpness of Young’s inequality for convolution, Math. Scand. 53, 221-237, 1983.
  • [20] M. Rajagopalan, $L^p$-conjecture for locally compact groups-I, Trans. Amer. Math. Soc. 125, 216-222, 1966
  • [21] M. Rajagopalan and W Zelazko, $L^p$-conjecture for solvable locally compact groups, J. Indian Math. Soc. 29, 87-93, 1965.
  • [22] M.M. Rao and Z.D. Ren, Theory of Orlicz Spaces, Marcel Dekker, New York, 1991.
  • [23] S. Saeki, The $L^p$-conjecture and Young’s inequality, Illinois Journal of Mathematics, 34(3), 614-627, 1990.
  • [24] S.M. Tabatabaie and A.R. Bagheri Salec, Convolution of two weighted Orlicz spaces on hypergroups, Revista Colombiana de Matemáticas, 54(2), 117-128, 2020.
  • [25] S.M. Tabatabaie, A.R. Bagheri Salec and M. Zare Sanjari, A note on Orlicz algebras, Oper. Matrices, 14(1), 139-144, 2020.
  • [26] S.M. Tabatabaie and A.R. Bagheri Salec, On The inclusion of X spaces, Mathematica Bohemica, 148(1), 65-72, 2023.
Year 2024, Volume: 53 Issue: 1, 191 - 200, 29.02.2024
https://doi.org/10.15672/hujms.1018098

Abstract

References

  • [1] A.R. Bagheri Salec and S.M. Tabatabaie, Some necessary and sufficient conditions for convolution weighted Orlicz algebras, Bull. Iranian Math. Soc. 48, 2509-2520, 2022.
  • [2] A.R. Bagheri Salec, S. Ivkovic and S.M. Tabatabaie, Spaceability on some classes of Banach spaces, Math. Ineq. Appl. 25(3), 659-672, 2022.
  • [3] A.R. Bagheri Salec, V. Kumar and S.M. Tabatabaie, Convolution properties of Orlicz spaces on hypergroups, Proc. Amer. Math. Soc. 150(4), 1685-1696, 2022.
  • [4] L. Bernal-González and M.O. Cabrera, Spaceability of strict order integrability, J. Math. Anal. Appl. 385, 303-309, 2012.
  • [5] R. del Campo, A. Fernández, F. Mayoral and F. Naranjo, Orlicz spaces associated to a quasi-Banach function space. Applications to vector measures and interpolation, Collect. Math. 72, 481-499, 2021.
  • [6] S. Glab and F. Strobin, Dichotomies for $L^p$ spaces, J. Math. Anal. Appl. 368, 382-390, 2010.
  • [7] S. Glab and F. Strobin, Spaceability of sets in $L^p\times L^q$ and $C_0\times C_0$, J. Math. Anal. Appl. 440, 451-465, 2016.
  • [8] H. Hudzik, Orlicz spaces of essentially bounded functions and Banach-Orlicz algebras, Arch. Math. 44, 535-538, 1985.
  • [9] H. Hudzik, A. Kamiska and J. Musielak, On some Banach algebras given by a modular, in: Alfred Haar Memorial Conference, Budapest, Colloquia Mathematica Societatis J anos Bolyai (North Holland, Amsterdam), 49, 445-463, 1985.
  • [10] P. Jain, L.E. Persson and P. Upreti, Inequalities and properties of some generalized Orlicz classes and spaces, Acta Math. Hungar. 117, 161-174, 2007.
  • [11] V. Kumar, R. Sarma and N. Shravan Kumar, Orlicz algebras on homogeneous spaces of compact groups and their abstract linear representations, Mediterr. J. Math. 15(4), 186, 2018.
  • [12] V. Kumar, R. Sarma and N. Shravan Kumar, Orlicz spaces on hypergroups, Publ. Math. Debrecen 94(1-2), 31-47, 2019.
  • [13] L. Maligranda and L.E. Persson, Generalized duality of some Banach function spaces, Proc. Konin. Nederlands Akad. Wet. 92, 323-338, 1989.
  • [14] S. Okada, W. Ricker, and E.A. Sánchez-Pérez, Optimal domain and integral extension of operators acting in functions spaces, Operator Theory: Advances and Applications, vol. 180, Birkhäuser, Verlag, Besel, 2008.
  • [15] A. Osançlıol and S. Öztop, Weighted Orlicz algebras on locally compact groups, J. Aust. Math. Soc. 99, 399-414, 2015.
  • [16] S. Öztop and S.M. Tabatabaie, Weighted Orlicz algebras on hypergroups, FILOMAT, 34(7), 2131-2139, 2020.
  • [17] L. E. Persson, Some elementary inequalities in connection with Xp-spaces, in: Constructive Theory of Functions, 367-376, 1988.
  • [18] L. E. Persson, On some generalized Orlicz classes and spaces, Research Report 1988-3, Department of Mathematics, Lulea University of Technology, 1988.
  • [19] T.S. Quek and L.Y.H. Yap, Sharpness of Young’s inequality for convolution, Math. Scand. 53, 221-237, 1983.
  • [20] M. Rajagopalan, $L^p$-conjecture for locally compact groups-I, Trans. Amer. Math. Soc. 125, 216-222, 1966
  • [21] M. Rajagopalan and W Zelazko, $L^p$-conjecture for solvable locally compact groups, J. Indian Math. Soc. 29, 87-93, 1965.
  • [22] M.M. Rao and Z.D. Ren, Theory of Orlicz Spaces, Marcel Dekker, New York, 1991.
  • [23] S. Saeki, The $L^p$-conjecture and Young’s inequality, Illinois Journal of Mathematics, 34(3), 614-627, 1990.
  • [24] S.M. Tabatabaie and A.R. Bagheri Salec, Convolution of two weighted Orlicz spaces on hypergroups, Revista Colombiana de Matemáticas, 54(2), 117-128, 2020.
  • [25] S.M. Tabatabaie, A.R. Bagheri Salec and M. Zare Sanjari, A note on Orlicz algebras, Oper. Matrices, 14(1), 139-144, 2020.
  • [26] S.M. Tabatabaie and A.R. Bagheri Salec, On The inclusion of X spaces, Mathematica Bohemica, 148(1), 65-72, 2023.
There are 26 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Mathematics
Authors

Chung-chuan Chen 0000-0003-4297-3305

Alireza Bagheri Salec 0000-0002-4917-6125

Seyed Mohammad Tabatabaie 0000-0003-4392-2577

Early Pub Date August 15, 2023
Publication Date February 29, 2024
Published in Issue Year 2024 Volume: 53 Issue: 1

Cite

APA Chen, C.-c., Bagheri Salec, A., & Tabatabaie, S. M. (2024). Orlicz algebras associated to a Banach function space. Hacettepe Journal of Mathematics and Statistics, 53(1), 191-200. https://doi.org/10.15672/hujms.1018098
AMA Chen Cc, Bagheri Salec A, Tabatabaie SM. Orlicz algebras associated to a Banach function space. Hacettepe Journal of Mathematics and Statistics. February 2024;53(1):191-200. doi:10.15672/hujms.1018098
Chicago Chen, Chung-chuan, Alireza Bagheri Salec, and Seyed Mohammad Tabatabaie. “Orlicz Algebras Associated to a Banach Function Space”. Hacettepe Journal of Mathematics and Statistics 53, no. 1 (February 2024): 191-200. https://doi.org/10.15672/hujms.1018098.
EndNote Chen C-c, Bagheri Salec A, Tabatabaie SM (February 1, 2024) Orlicz algebras associated to a Banach function space. Hacettepe Journal of Mathematics and Statistics 53 1 191–200.
IEEE C.-c. Chen, A. Bagheri Salec, and S. M. Tabatabaie, “Orlicz algebras associated to a Banach function space”, Hacettepe Journal of Mathematics and Statistics, vol. 53, no. 1, pp. 191–200, 2024, doi: 10.15672/hujms.1018098.
ISNAD Chen, Chung-chuan et al. “Orlicz Algebras Associated to a Banach Function Space”. Hacettepe Journal of Mathematics and Statistics 53/1 (February 2024), 191-200. https://doi.org/10.15672/hujms.1018098.
JAMA Chen C-c, Bagheri Salec A, Tabatabaie SM. Orlicz algebras associated to a Banach function space. Hacettepe Journal of Mathematics and Statistics. 2024;53:191–200.
MLA Chen, Chung-chuan et al. “Orlicz Algebras Associated to a Banach Function Space”. Hacettepe Journal of Mathematics and Statistics, vol. 53, no. 1, 2024, pp. 191-00, doi:10.15672/hujms.1018098.
Vancouver Chen C-c, Bagheri Salec A, Tabatabaie SM. Orlicz algebras associated to a Banach function space. Hacettepe Journal of Mathematics and Statistics. 2024;53(1):191-200.