Characterization of the restricted type spaces R(X)

2012/11/14 by Javier Soria, Soria, Javier, Pedro Tradacete +1
Mathematics · #26D10 #46E30 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #math.CA #math.FA #msc:26D10 #msc:46E30

paper · pdf · doi:10.48550/arxiv.1211.3386

21 pages

arxiv created 2013/11/14 · arxiv updated 2013/11/15

Abstract

We study functorial properties of the spaces R(X), introduced in [Studia Math. 197 (2010), 69-79] as a central tool in the analysis of the Hardy operator minus the identity on decreasing functions. In particular, we provide conditions on a minimal Lorentz space Λ_φ so that the equation R(X)=Λ_φ has a solution within the category of rearrangement invariant (r.i.) spaces. Moreover, we show that if R(X)=Λ_φ, then we can always take X to be the minimal r.i. Banach range space for the Hardy operator defined in Λ_φ.

Related

• New Lorentz spaces for the restricted weak-type Hardy's inequalities
• Optimal domain for the Hardy operator
• Characterization of rearrangement invariant spaces with fixed points for the Hardy-Littlewood maximal operator
• Rearrangement invariant optimal range for Hardy type operators
• A few notes on Lorentz spaces