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

Examples of Fourier Multipliers of the Sobolev Space W 1,1 (ℝ d )

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Examples of Fourier Multipliers of the Sobolev Space W 1,1 (ℝ d )