Abstract
In the mid of 70s, L.G.Gurov and Yu.G.Reshetnyak introduced in analogy with the definition of BMO the class which consists of all non-negative integrable on cube functions whose integral oscillations does not exceed small constant times integral means over all subcubes of the domain. This class has found interesting applications in quasi-conformal mappings and PDE's. In a joint work with A.A. Korenovskiy and A.K. Lerner we established an equivalence between the Gurov-Reshetnyak and Muckehoupt's A-infinity conditions for arbitrary absolutely continuous measures. Also, we studied maximal Gurov-Reshetnyak condition and proved that for a large class of measures satisfying Busemann-Feller type condition, it will be self-improving as the usual Gurov-Reshetnyak condition. This answers to a question raised by T.Iwaniec and V.I.Kolyada.
| Original language | American English |
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| State | Published - Jun 2005 |
| Event | Harmonic Analysis and Partial Differential Equations Workshop - Kiel, Germany Duration: Jun 1 2005 → … |
Conference
| Conference | Harmonic Analysis and Partial Differential Equations Workshop |
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| Period | 06/1/05 → … |
Keywords
- Gurov-Reshetnyak Property
DC Disciplines
- Mathematics