CAS Seminar

Victor Kolyada

(Karlstad University)

"Iterated rearrangements and Gagliardo-Sobolev type inequalities"

Date: Wed, November 23, 2011
Time: 11:15
Place: Research I Seminar room

Abstract: We consider Lorentz type spaces ℒp,rσ defined in terms of iterated rearrangements of functions of several variables (σ is a permutation of {1,...,n}). Further, we study Fournier-Gagliardo mixed norm spaces 𝒱(ℝn) closely related to Sobolev spaces W11(ℝn). We prove estimate of ‖ f ‖n',1σ via ‖ f ‖𝒱 with the sharp constant. In particular, this gives a refinement of the known Sobolev type inequalities for the space W11(ℝn). Abstract in pdf.