On the Iterated Integral Operators on the Cone of Monotone Functions

被引:0
作者
V. D. Stepanov [1 ]
G. E. Shambilova [2 ]
机构
[1] FEB RAS Computing Center, Khabarovsk
[2] Steklov Mathematical Institute, Moscow
[3] Moscow State University of Civil Engineering, Moscow
基金
俄罗斯科学基金会;
关键词
517.51; bilinear integral operator; cone of monotone functions; weighted Lebesgue space;
D O I
10.1134/S0037446625020119
中图分类号
学科分类号
摘要
We characterize the quasilinear integral operators of iterated typeon the cone of nondecreasing functions in Lebesgue spaces on the real semiaxis. © Pleiades Publishing, Ltd. 2025.
引用
收藏
页码:345 / 363
页数:18
相关论文
共 29 条
  • [1] Arino M., Muckenhoupt B., Maximal functions on classical Lorentz spaces and Hardy’s inequality with weights for nonincreasing functions, Trans. Amer. Math. Soc, 320, 2, pp. 727-735, (1990)
  • [2] Sawyer E., Boundedness of classical operators on classical Lorentz spaces, Studia Math, 96, 2, pp. 145-158, (1990)
  • [3] Stepanov V.D., The weighted Hardy’s inequality for nonincreasing functions, Trans. Amer. Math. Soc, 338, 1, pp. 173-186, (1993)
  • [4] Stepanov V.D., Integral operators on the cone of monotone functions, J. Lond. Math. Soc. (2), 48, 3, pp. 465-487, (1993)
  • [5] Carro M., Soria J., Weighted Lorentz spaces and the Hardy operator, J. Funct. Anal, 112, 2, pp. 480-494, (1993)
  • [6] Carro M., Soria J., Boundedness of some integral operators, Canad. J. Math, 45, 6, pp. 1155-1166, (1993)
  • [7] Goldman M.L., Heinig H.P., Stepanov V.D., On the principle of duality in Lorentz spaces, Canad. J. Math, 48, 5, pp. 959-979, (1996)
  • [8] Sinnamon G., Embeddings of concave functions and duals of Lorentz spaces, Publ. Mat, 46, 2, pp. 489-515, (2002)
  • [9] Gogatishvili A., Stepanov V.D., Integral operators on cones of monotone functions, Dokl. Math, 86, 2, pp. 650-653, (2012)
  • [10] Gogatishvili A., Stepanov V.D., Reduction theorems for operators on the cones of monotone functions, J. Math. Anal. Appl, 405, 1, pp. 156-172, (2013)