Equivalent definitions of dyadic Muckenhoupt and reverse Holder classes in terms of Carleson sequences, weak classes, and comparability of dyadic L log L and A(infinity) constants

摘要

In the dyadic case the union of the reverse Holder classes, Up>1RHpd, is strictly larger than the union of the Muckenhoupt classes, U(p>1)A(p)(d) = A(infinity)(d). We introduce the RH1d condition as a limiting case of the RHpd inequalities as p tends to 1 and show the sharp bound on the RH1d constant of the weight w in terms of its A(infinity)(d) constant.