The sharp weighted bound for general Calderón-Zygmund operators

摘要: For a general Calderon‐Zygmund operator T on R N , it is shown that kTfkL2(w) C(T) sup Q A w 1 k fkL2(w) for all Muckenhoupt weights 2 A2. This optimal estimate was known as the A2 conjecture. recent result of Perez‐Treil‐Volberg reduced problem to testing condition indicator functions, which verified in this paper. The proof consists following elements: (i) variant Nazarov‐ Treil‐Volberg method random dyadic systems with just one system and completely without “bad” parts; (ii) resulting representation an average “dyadic shifts;” (iii) improvements Lacey‐Petermichl‐Reguera estimates these shifts, allow summing up series obtained representation.