Exact Calculation of Sums of Cones in Lorentz Spaces

被引：5
作者：
Berezhnoi, E. I. [1 ]
机构：
[1] Yaroslavl State Univ, Yaroslavl, Russia
来源：
FUNCTIONAL ANALYSIS AND ITS APPLICATIONS | 2018年 / 52卷 / 02期
关键词：
sum of cones in Lorentz space; extrapolation theorem; EXTRAPOLATION;
D O I：
10.1007/s10688-018-0218-3
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A method for exactly calculating norm on the sum of the cones of nonincreasing or concave functions in Lorentz spaces is proposed. The obtained result makes it possible to prove new extrapolation theorems for cones in Lorentz, Lebesgue, and Marcinkiewicz spaces with exact constants.
引用
收藏
页码：134 / 138
页数：5
相关论文
共 13 条
  • [1] [Anonymous], 1979, ERGEBNISSE MATH IHRE
  • [2] [Anonymous], 1993, T MAT I STEKLOV
  • [3] MAXIMAL FUNCTIONS ON CLASSICAL LORENTZ SPACES AND HARDY INEQUALITY WITH WEIGHTS FOR NONINCREASING FUNCTIONS
    ARINO, MA
    MUCKENHOUPT, B
    [J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1990, 320 (02) : 727 - 735
  • [4] Bennett C., 1988, Interpolation of operators
  • [5] Berezhnoi E. I., 2006, DOKL ROSS AKAD NAUK, V406, P43
  • [6] Extrapolation on the cone of decreasing functions
    Carro, Maria J.
    Marcoci, Anca N.
    Marcoci, Liviu G.
    [J]. JOURNAL OF APPROXIMATION THEORY, 2012, 164 (05) : 776 - 790
  • [7] Fiorenza A, 2004, Z ANAL ANWEND, V23, P657
  • [8] Fiorenza A., 2000, Collect. Math., V51, P131
  • [9] Reduction theorems for weighted integral inequalities on the cone of monotone functions
    Gogatishvili, A.
    Stepanov, V. D.
    [J]. RUSSIAN MATHEMATICAL SURVEYS, 2013, 68 (04) : 597 - 664
  • [10] Extrapolation theory: new results and applications
    Karadzhov, GE
    Milman, M
    [J]. JOURNAL OF APPROXIMATION THEORY, 2005, 133 (01) : 38 - 99
12