Muckenhoupt weights with singularities on closed lower dimensional sets in spaces of homogeneous type

AIMAR, HUGO; CARENA. MARILINA; TOSCHI, MARISA

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

ACADEMIC PRESS INC ELSEVIER SCIENCE

Lugar: Amsterdam; Año: 2014 vol. 416 p. 112 - 125

0022-247X

egin{abstract} We give sufficient conditions on a real number $eta$ and on a closed set $F$ in a general space of homogeneous type $(X,d,mu)$ in such a way that $mu(B(x,d(x,F)))^eta$ becomes a Muckenhoupt weight. In order to prove our result, we modify the underlying space so that it becomes $1$-Ahlfors regular. end{abstract}