Let

be a positive Borel measure on a space of homogeneous type (X, d,

), satisfying the doubling property. A condition on a weight

for whixh a maximal operator

(x) defined by M

f(x)=supr>0{{{{ { 1} over {ν(B(x,r)) } INT _{ B(x,r)} │f(y)│d mu (y)}}}}, is of weak type (p,p) with respect to (ν,

), is that there exists a constant C such that C

(y) for a.e. y

B(x, r) if p=1, and {{{{( { 1} over { upsilon (B(x,r) } INT _{ B(x,r)}omega(y) ^ (-1/p-1) d mu (y))^(p-1)}}}} C, if 1

.