On a class of Mikhlin multipliers which do not preserve $L^1$-, $L^{\infty }$-regularity and continuity

Pavel Dimovski, Stevan Pilipovic, Bojan Prangoski

We show that every Fourier multiplier with real-valued and positively homogeneous symbol of order 0, supported in a cone whose dual cone has a nonempty interior and such that the a…