Let G be a locally compact Abelian group (noncompact and nondiscrete) with Haar measure. Suppose that 1 < p < ∞ and 1 ≤ q ≤ ∞. The purpose of the paper is to define temperate Lorentz spaces and study the spaces of multipliers on Lorentz spaces and characterize them as the spaces of multipliers of certain Banach algebras.
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References
A. P. Blozinski, “On a convolution theorem for L(p, q) spaces,” Trans. Amer. Math. Soc., 164, 255–264 (1972).
Y. K. Chen and H. C. Lai, “Multipliers of Lorentz spaces,” Hokkaido Math. J., 4, 247–260 (1975).
R. S. Doran and J. Wichmann, “Approximate identities and factorization in Banach modules,” Lect. Notes Math., 305 (1979).
H. G. Feichtinger, “Multipliers of Banach spaces of functions on groups,” Math. Z., 152, 47–58 (1976).
E. V. Ferreyra, “Weighted Lorentz norm inequalities for integral operators,” Stud. Math., 96, 125–134 (1990).
J. Griffin and K. McKennon, “Multipliers and group Lp-algebras,” Pacif. J. Math., 49, 365–370 (1973).
E. Hewitt and K. A. Ross, Abstract Harmonic Analysis, Springer, Berlin (1963), Vol. 1.
E. Hewitt and K. A. Ross, Abstract Harmonic Analysis, Springer, Berlin (1970), Vol. 2.
R. A. Hunt, “On L(p, q) spaces,” L’enseignement Math., 12, No. 4, 249–276 (1966).
R. Larsen, An Introduction to the Theory of Multipliers, Springer, Berlin–Heidelberg (1971).
K. McKennon, “Multipliers of type (p, p),” Pacif. J. Math., 43, 429–436 (1972).
K. McKennon, “Multipliers of type (p, p) and multipliers of group algebras,” Pacif. J. Math., 45, 297–302 (1973).
K. McKennon, “Corrections to [5], [9], and [10],” Pacif. J. Math., 61, 603–606 (1975).
R. O’Neil, “Convolution operators and L(p, q) spaces,” Duke Math. J., 30, 129–142 (1963).
S. Ö ztop, “A note on multipliers of L p (G,A),” J. Austral. Math. Soc., 74, 25–34 (2003).
H. C. Wang, Homogeneous Banach Algebras, Marcel Dekker, New York (1977).
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 67, No. 3, pp. 341–354, March, 2015.
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Eryılmaz, İ., Duyar, C. Investigation of the Functional Properties and Spaces of Multipliers for Group L(p, q)(G)-Algebras. Ukr Math J 67, 390–407 (2015). https://doi.org/10.1007/s11253-015-1088-y
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DOI: https://doi.org/10.1007/s11253-015-1088-y