CARLESON MEASURES AND SQUARE FUNCTIONS: LINEAR, BILINEAR AND SOME PROBLEMS LUCAS OLIVEIRA The use of square functions for obtaining information about boundedness of singular integrals and maximal Fourier multipliers is a classical topic in Harmonic analysis, at least in situation where the operators are linear. In this talk we discuss what can be said about extensions of this kind results to the bilinear case. D EPARTMENTO DE M ATEM ÁTICA , U NIVERSIDADE F EDERAL P ORTO A LEGRE RS 91.509-900 E-mail address: [email protected] 1 DO R IO G RANDE DO S UL ,