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| 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 ‖ℒn',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.