Boundedness Of Some Operators And Composition Of Maximal Operators On Spaces Of Homogeneous Type

The triple ( X , d ,μ) is said to be a space of homogeneous type, if X be a set endowed with a positive Borel regular measureμand a symmetric quasi-metric d. Moreover,μsatisfies the following doubling condition: there exists a constant C≥1 such that for all x∈X and r > 0,μ(B(x, 2r ))≤Cμ(B(x, r)) <∞,where B ( x , r ) = { y∈X : d ( x ,y )