Maximal Operators Associated with Vector Polynomials of Lacunary Coefficients

We prove the L(p)(R(d)) (1 < p <= infinity) boundedness of the maximal operators associated with a family of vector polynomials given by the form {(2(k1)p(1) (t),..., 2(kd)p(d)(t)) : t is an element of R}. Furthermore, by using the lifting argument, we extend this result to a general class of vector polynomials whose coefficients are of the form constant times 2(k).