  In this paper we study some estimates of norms in variable exponent Lebesgue
spaces for a singular integral operators that are imaginary powers of the
Laplace operator in $\R^n$. Using Mellin transform argument, from this
estimates we obtain boundedness for a family of maximal operators in variable
exponent Lebesgue spaces, which are closely related to the (weak) solution of
the wave equation.42B25, 42B20, 46E30, 44A10, 42B10, 35L05
