On equivalent criteria for the boundedness of Hardy type operators on the cone of decreasing functions

M. Arino and B. Muckenhoupt, Maximal functions on classical Lorentz spaces and Hardy’s inequality with weights for non-increasing functions, Trans. Amer. Math. Soc., 320(1990), 727–735.

G. Bennett and K.-G. Grosse-Erdmann, Weighted Hardy inequalities for decreasing sequences and functions, Math. Annalen, 334(2006), 489–531.

M. Carro, A. Gogatishvili, J. Martin, and L. Pick, Inequalities involving two Hardy operators with applications to embeddings of function spaces, J. Operator Theory, 59(2008), 309–332.

M. L. Goldman, On integral inequalities on a set of functions with some properties of monotonicity, Function Spaces, Differential Operators and Nonlinear Analysis, Teubner (Leipzig, 1993), 274–279.

M. L. Goldman, Hardy type inequalities on the cone of quasimonotone functions, Russ. Acad. Sci. Far-East Branch Computer Center, Res. Rep. no 98/31 (1998), 1–69.

M. L. Goldman, Two-sided estimates for integral operators on the cone, Spectral and Evolution Problems, Proc. of 10th Crimean Autumn Math. School-Symposium, Simferopol, Nation. Univ. Tavridy (2000), 16–19.

M. L. Goldman, Sharp estimates of the norms of Hardy type operators on the cone of quasimonotone functions, Proc. Steklov Inst. Math., 232(2001), 109–137.

M. L. Goldman, Estimates of norms of Hardy type integral and discrete operators on cones of quasimonotone functions, Doklady Math., 63(2001), No. 2, 250–255.

E. Sawyer, Boundedness of classical operators on classical Lorentz spaces, Studia Math., 96(1990), 145–158.

V. D. Stepanov, On integral operators on the cone of monotone functions and on the embeddings of Lorentz spaces, Doklady Akad. Nauk SSSR, 317(1991), No. 6, 1308–1311.

V. D. Stepanov, The weighted Hardy inequality for non-increasing functions, Trans. Amer. Math. Soc., 338(1993), 173–186.

V. D. Stepanov, Integral operators on the cone of monotone functions, J. London Math. Soc., 48(1993), 465–487.