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Year 2023, Volume: 52 Issue: 5, 1198 - 1205, 31.10.2023
https://doi.org/10.15672/hujms.1175682

Abstract

References

  • [1] I. Akbarbaglu and S. Maghsoudi, Banach-Orlicz algebras on a locally compact group, Mediterr. J. Math. 10, 1937-1974, 2013.
  • [2] G. Bennet and R. Sharpley, Interpolation of Operators, Academic Press London, 1988.
  • [3] Z.W. Birnbaum and W. Orlicz, Über die Verallgemeinerung des Begriffes der zueinander konjugerten Potenzen, Studia Math. 3, 1-67, 1931.
  • [4] O. Blasco and A. Osançlıol, Notes on bilinear multipliers on Orlicz spaces, Math. Nachr. 292 (12), 2522-2536, 2019.
  • [5] B. Brainerd and R. E. Edwards, Linear operators which commute with translations I. Representation theorems, J. Aust. Math. Soc. 6, 289-327, 1966.
  • [6] A. Cianchi, L. Pick and L. Slavíkova, Sobolev embeddings in Orlicz and Lorentz spaces with measures, J. Math. Anal. Appl. 485, Paper no. 123827, 2020.
  • [7] P. Harjulehto and P. Hästö, Orlicz Spaces and Generalized Orlicz Spaces, Lecture notes in mathematics, 2236, Springer, 2019.
  • [8] E. Kaniuth and K.F. Taylor, Induced representations of locally compact groups, Cambridge University Press, 197, 2013.
  • [9] M.A. Krasnosel’skii and Ja.B. Rutickii, Convex Functions and Orlicz Spaces, Noordhoff, Graningen, 1961.
  • [10] R. Larsen, An Introduction to the Theory of Multipliers, Die Grundlehren der mathematischen Wissenschaften, 175, Springer-Verlag, Berlin, Heidelberg and New York, 1971.
  • [11] A.T. Lau, Closed convex invariant subsets of Lp(G), Trans. Am. Math. Soc. 232, 131-142, 1977.
  • [12] W.A.J. Luxemburg, Banach function spaces, PhD Dissertation, 1955.
  • [13] W.A. Majewski and L.E. Labuschagne, On applications of Orlicz spaces to statistical physics, Ann. Henri Poincaré 15, 1197-1221, 2014.
  • [14] W. Orlicz, Über eine gewisse klasse von Räumen vom Typus B, Bulletin International de l’Academie Polonaise des Sciences et des Lettres Série A, 8, 207-220, 1932.
  • [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 E. Samei, Twisted Orlicz algebras I, Studia Math. 236, 271-296, 2017.
  • [17] S. Öztop and E. Samei, Twisted Orlicz algebras II, Math. Nachr. 292, 1122-1136, 2019.
  • [18] M.M. Rao and Z.D. Ren, Theory of Orlicz Spaces, Marcel Dekker, New York, 1991.
  • [19] R. Üster and S. Öztop, Invariant subsets and homological properties of Orlicz modules over group algebras, Taiwan. J. Math. 24, 959-973, 2020.
  • [20] R. Üster, Multipliers for the weighted Orlicz spaces of a locally compact abelian group, Results in Math. 76 (4), Paper No. 183, 2021.
  • [21] J. Wendel, Left centralizers and isomorphisms of group algebras Pac. J. Math. 2, 251-261, 1952.

A criterion for nonzero multiplier for Orlicz spaces of an affine group $\mathbb{R}_{+}\times \mathbb{R}$

Year 2023, Volume: 52 Issue: 5, 1198 - 1205, 31.10.2023
https://doi.org/10.15672/hujms.1175682

Abstract

Let $\mathbb{A}=\mathbb{R}_{+}\times \mathbb{R}$ be an affine group with right Haar measure $d\mu$ and $\Phi_i$, $i=1,2$, be Young functions. We show that there exists an isometric isomorphism between the multiplier of the pair $(L^{\Phi_1}(\mathbb{A}),L^{\Phi_2}(\mathbb{A}))$ and $(L^{\Psi_2}(\mathbb{A}),L^{\Psi_1}(\mathbb{A}))$ where $\Psi_i$ are complementary pairs of $\Phi_i$, $i=1,2$, respectively. Moreover we show that under some conditions there is no nonzero multiplier for the pair $(L^{\Phi_1}(\mathbb{A}),L^{\Phi_2}(\mathbb{A}))$, i.e., for an affine group $\mathbb{A}$ only the spaces $M(L^{\Phi_1}(\mathbb{A}),L^{\Phi_2}(\mathbb{A}))$, with a concrete condition, are of any interest.

References

  • [1] I. Akbarbaglu and S. Maghsoudi, Banach-Orlicz algebras on a locally compact group, Mediterr. J. Math. 10, 1937-1974, 2013.
  • [2] G. Bennet and R. Sharpley, Interpolation of Operators, Academic Press London, 1988.
  • [3] Z.W. Birnbaum and W. Orlicz, Über die Verallgemeinerung des Begriffes der zueinander konjugerten Potenzen, Studia Math. 3, 1-67, 1931.
  • [4] O. Blasco and A. Osançlıol, Notes on bilinear multipliers on Orlicz spaces, Math. Nachr. 292 (12), 2522-2536, 2019.
  • [5] B. Brainerd and R. E. Edwards, Linear operators which commute with translations I. Representation theorems, J. Aust. Math. Soc. 6, 289-327, 1966.
  • [6] A. Cianchi, L. Pick and L. Slavíkova, Sobolev embeddings in Orlicz and Lorentz spaces with measures, J. Math. Anal. Appl. 485, Paper no. 123827, 2020.
  • [7] P. Harjulehto and P. Hästö, Orlicz Spaces and Generalized Orlicz Spaces, Lecture notes in mathematics, 2236, Springer, 2019.
  • [8] E. Kaniuth and K.F. Taylor, Induced representations of locally compact groups, Cambridge University Press, 197, 2013.
  • [9] M.A. Krasnosel’skii and Ja.B. Rutickii, Convex Functions and Orlicz Spaces, Noordhoff, Graningen, 1961.
  • [10] R. Larsen, An Introduction to the Theory of Multipliers, Die Grundlehren der mathematischen Wissenschaften, 175, Springer-Verlag, Berlin, Heidelberg and New York, 1971.
  • [11] A.T. Lau, Closed convex invariant subsets of Lp(G), Trans. Am. Math. Soc. 232, 131-142, 1977.
  • [12] W.A.J. Luxemburg, Banach function spaces, PhD Dissertation, 1955.
  • [13] W.A. Majewski and L.E. Labuschagne, On applications of Orlicz spaces to statistical physics, Ann. Henri Poincaré 15, 1197-1221, 2014.
  • [14] W. Orlicz, Über eine gewisse klasse von Räumen vom Typus B, Bulletin International de l’Academie Polonaise des Sciences et des Lettres Série A, 8, 207-220, 1932.
  • [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 E. Samei, Twisted Orlicz algebras I, Studia Math. 236, 271-296, 2017.
  • [17] S. Öztop and E. Samei, Twisted Orlicz algebras II, Math. Nachr. 292, 1122-1136, 2019.
  • [18] M.M. Rao and Z.D. Ren, Theory of Orlicz Spaces, Marcel Dekker, New York, 1991.
  • [19] R. Üster and S. Öztop, Invariant subsets and homological properties of Orlicz modules over group algebras, Taiwan. J. Math. 24, 959-973, 2020.
  • [20] R. Üster, Multipliers for the weighted Orlicz spaces of a locally compact abelian group, Results in Math. 76 (4), Paper No. 183, 2021.
  • [21] J. Wendel, Left centralizers and isomorphisms of group algebras Pac. J. Math. 2, 251-261, 1952.
There are 21 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Mathematics
Authors

Rüya Üster 0000-0003-4063-5118

Publication Date October 31, 2023
Published in Issue Year 2023 Volume: 52 Issue: 5

Cite

APA Üster, R. (2023). A criterion for nonzero multiplier for Orlicz spaces of an affine group $\mathbb{R}_{+}\times \mathbb{R}$. Hacettepe Journal of Mathematics and Statistics, 52(5), 1198-1205. https://doi.org/10.15672/hujms.1175682
AMA Üster R. A criterion for nonzero multiplier for Orlicz spaces of an affine group $\mathbb{R}_{+}\times \mathbb{R}$. Hacettepe Journal of Mathematics and Statistics. October 2023;52(5):1198-1205. doi:10.15672/hujms.1175682
Chicago Üster, Rüya. “A Criterion for Nonzero Multiplier for Orlicz Spaces of an Affine Group $\mathbb{R}_{+}\times \mathbb{R}$”. Hacettepe Journal of Mathematics and Statistics 52, no. 5 (October 2023): 1198-1205. https://doi.org/10.15672/hujms.1175682.
EndNote Üster R (October 1, 2023) A criterion for nonzero multiplier for Orlicz spaces of an affine group $\mathbb{R}_{+}\times \mathbb{R}$. Hacettepe Journal of Mathematics and Statistics 52 5 1198–1205.
IEEE R. Üster, “A criterion for nonzero multiplier for Orlicz spaces of an affine group $\mathbb{R}_{+}\times \mathbb{R}$”, Hacettepe Journal of Mathematics and Statistics, vol. 52, no. 5, pp. 1198–1205, 2023, doi: 10.15672/hujms.1175682.
ISNAD Üster, Rüya. “A Criterion for Nonzero Multiplier for Orlicz Spaces of an Affine Group $\mathbb{R}_{+}\times \mathbb{R}$”. Hacettepe Journal of Mathematics and Statistics 52/5 (October 2023), 1198-1205. https://doi.org/10.15672/hujms.1175682.
JAMA Üster R. A criterion for nonzero multiplier for Orlicz spaces of an affine group $\mathbb{R}_{+}\times \mathbb{R}$. Hacettepe Journal of Mathematics and Statistics. 2023;52:1198–1205.
MLA Üster, Rüya. “A Criterion for Nonzero Multiplier for Orlicz Spaces of an Affine Group $\mathbb{R}_{+}\times \mathbb{R}$”. Hacettepe Journal of Mathematics and Statistics, vol. 52, no. 5, 2023, pp. 1198-05, doi:10.15672/hujms.1175682.
Vancouver Üster R. A criterion for nonzero multiplier for Orlicz spaces of an affine group $\mathbb{R}_{+}\times \mathbb{R}$. Hacettepe Journal of Mathematics and Statistics. 2023;52(5):1198-205.

Cited By

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