Pasting Muckenhoupt weights through a contact point between sets of different dimensions

Abstract

We extend the result in Bernd S. W. Schr¨oder, On pasting Ap-weights, Proc. Amer. Math. Soc., 124 (1996), 3339?3344, to the spaces of homogeneous type, built in Hugo Aimar and Liliana Nitti, Separation and contact of sets of different dimensions in a doubling environment, Publ. Math. Debrecen, 74 (2009), 351?368, starting from two sets of different dimensions with a unique point of contact.