Matrix-weighted fractional type operators on spaces of homogeneous type

Abstract In this paper, we introduce matrix <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msub> <m:mi>A</m:mi> <m:mrow> <m:mi>p</m:mi> <m:mo>,</m:mo> <m:mi>q</m:mi> </m:mrow> </m:msub> </m:math> {A_{p,q}} weights on spaces of homogeneous type in the sense of Coifman and Weiss, and prove some basic properties of these weights. As applications, the necessary and sufficient condition for the boundedness of matrix-weighted fractional maximal operators on Lebesgue spaces is established, and the boundedness of matrix-weighted fractional integral operators on Lebesgue spaces is obtained.