Weight Dependent Convolution on Beurling Spaces and Multipliers
DOI:
https://doi.org/10.5644/SJM.19.02.03Keywords:
weight, Beurling space, convolution, Banach algebra, multiplierAbstract
In this paper, some properties of a generalized translation operator are obtained. A weight dependent convolution product on Beurling spaces is studied. A convolution theorem related to a weight Fourier transform is obtained. Multipliers for the pair
$(\mathcal{L}_{\omega}^{1}(G),\mathcal{L}_{\omega}^{p}(G))$ are introduced.
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References
R. P. Agarwal, M. Meehan and D. O'Regan, Fixed Point Theory and Applications, Cambridge Univ. Press, United Kingdom, 2001.
A. Benazzouz, Contribution à l’analyse harmonique des algèbres de Beurling généralisées, Thèse de 3ème cycle, Faculté des Sciences de Rabat, 1986.
A. Bourouihiya, Beurling weighted spaces, product-convolution operators and the tensor product of frames, PhD thesis, University of Maryland, USA (2006).
G. B. Folland, A course in abstract harmonic analysis, CRC Press, Inc, 1995.
E. Hewitt K. A. Ross, Abstract Harmonic Analysis I, Springer-Verlag, (1979).
A. Issa, Y. Mensah, Multipliers on weighted group algebras, Gulf J. Math., 8(2), (2020), 35-45.
A. Issa, Y. Mensah, On Beurling spaces provided with a weight dependent convolution, Functional Analysis, vol. 1, (2022) ID 6.
E. Kaniuth, A course in commutative Banach algebras, Springer-Verlag, (2009).
A. EL Kinani, A. Roukbi, A. Benazzouz, Structure d'algèbre de Banach sur l'espace à poids $L_{omega}^{p}(G)$, Le Mathematiche, vol. LXIV (2009), Fasc. I, 179-193.
A. Mahmoodi, A new convolution on Beurling algebras, Math. Sci., vol. 3, No 9, (2009) 63-82.
H. Reiter, J. D. Stegeman, Classical harmonic analysis and locally compact groups, London Math. Society Monographs, vol. 22, Clarendon Press, Oxford, (2000).
