Basic properties and multipliers space on $L^1(G)cap L(P,q) (G)$ spaces

Basic properties and multipliers space on $L^1(G)cap L(P,q) (G)$ spaces

Let G be locally compact Abelian group with Haar measure. First is discussed some properties of $L^1(G)cap L(P,q) (G)$ spaces. Then is mentioned the multipliers space on $L^1(G)cap L(P,q) (G)$ spaces.

___

  • [1] Blozinski, A.P.: On a convolution theorem for L(p, q) spaces, Trans. Amer. Math. Soc. 164, 255-264, (1972).
  • [2] Blozinski, A.P.: Convolution of L(p, q) functions, Proc. of the Amer. Math. Soc. 32-1, 237-240, (1972).
  • [3] Chen, Y.K. and Lai, H.C.: Multipliers of Lorentz spaces, Hokkaido Math. J.4, 247-260, (1975).
  • [4] Duyar, C. and Gürkanlı, A.T.: Multipliers and Relative completion in weighted Lorentz spaces,Acta Math. Sci.23, 467-476, (2003).
  • [5] Feichtinger, H.: Multipliers of Banach spaces of functions on groups, Math. Z. 157, 47-58, (1976).
  • [6] Hunt, R.A.: On L(p, q) spaces, L’enseignement Mathematique,TXII-4, 249-276, (1966).
  • [7] O’Neil, R.: Convolution operators and L(p, q) spaces, DMJ 30, 129-142, (1963).
  • [8] Öztop, S.: A note on multipliers of $L^p (G,A)$, J. Aust. Math. Soc., 74, 25-34, (2003).
  • [9] Saeki, S. and Thome, E.L.: Lorentz spaces as $L^1$-modules and multipliers, Hokkaido Math. J. 23, 55-92, (1994).
  • [10] Wang, A.C.: Homogeneous Banach Algebras, M.Dekker INC.Newyork 1980.
  • [11] Warner, C.R.: Closed ideals in the group algebra $L^1 (G)cap L^2 (G)$, Trans. Amer. Math. Soc.,121,408-423, (1966).
  • [12] Yap, L.Y.H.: Some remarks on convolution operators and L(p, q) spaces, DMJ, 36, 647-658, (1969).
  • [13] Yap, L.Y.H.: Ideals in subalgebras of the group algebras, Studia Math. 35, 165-175, (1972).
  • [14] Yap, L.Y.H.: On Two classes of subalgebras of $L^1 (G)$, Proc. Japan Acad., 48, 315-319, (1972).