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Abstract
Coifman and Fefferman established that the class of Muckenhoupt weights is equivalent to the class of weights satisfying the "reverse Holder inequality". In a recent paper V. Vasyunin [17] presented a proof of the reverse Holder inequality with sharp constants for the weights satisfying the usual Muckenhoupt condition. In this paper we present the inverse, that is, we use the Bellman function technique to find the sharp A(p) constants for weights in a reverseHolder class on an interval; we also find the sharp constants for the higherintegrability result of Gehring [7].
Additionally, we find sharp bounds for the A(p) constants of reverseHolderclass weights defined on rectangles in Rn, as well as bounds on the A(p) constants for reverseHolder weights defined on cubes in Rn, without claiming the sharpness.
Original language  English 

Pages (fromto)  559594 
Number of pages  36 
Journal  Revista matematica iberoamericana 
Volume  25 
Issue number  2 
Publication status  Published  2009 
Keywords
 ReverseHolder class
 Gehring class
 A(p) weight
 Muckenhoupt weight
 Bellman function
 ELLIPTICEQUATIONS
 DIRICHLET PROBLEM
 MUCKENHOUPT
Projects
 1 Finished

Harmonic Analysis Technicques for partial differential equations in mathematical physics and geometry
1/11/05 → 30/04/08
Project: Research