The rearrangement-invariant space Gamma(p,phi)

作者：Gogatishvili Amiran; Kerman Ron^*

来源：Positivity, 2014, 18(2): 319-345.

DOI：10.1007/s11117-013-0246-4

• Lorentz Gamma space
• Kothe dual space
• Weighted norm inequalities
• Hardy operator
• Stieltjes transform
• Calderon-Zygmund operator

Fix and . Let be a positive measurable function on . Define the Lorentz Gamma norm, , at the measurable function by , in which , where , with . Our aim in this paper is to study the rearrangement-invariant space determined by . In particular, we determine its Kothe dual and its Boyd indices. Using the latter a sufficient condition is given for a Cald,ron-Zygmund operator to map such a space into itself.

• 出版日期2014-6