In this article we define and investigate a local Hardy-Littlewood maximal operator in Euclidean spaces. It is proved that this operator satisfies weighted L(p), p > 1, and weighted weak type (1, 1) estimates with weight function w is an element of A(loc)(p), the class of local A(p) weights which is larger than the Muckenhoupt A(p) class. Also, the condition w is an element of A(loc)(p) turns out to be necessary for the weighted weak type (p, p), p >= 1, inequality to hold.
