Abstract
Fourier multipliers of the space W1,1(ℝd) are bounded functions m such that the convolution by F−1m extends into a bounded operator on W1,1(ℝd). Poornima exhibited in the eighties a family of such Fourier multipliers among which some are not Fourier transforms of bounded measures for d > 1. Her counterexamples are based on celebrated non-inequalities of Ornstein. We will give new examples of Fourier multipliers, which are not Fourier transforms of measures and do not belong to her family. The examples are constructed on the d-dimensional torus and then transferred to the Euclidean space.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
