On the Wikipedia page, one can read that an iff condition for L1 boundedness of the Fourier multiplier m(D) is that $$ \hat m\quad\text{ is a Borel measure with finite total mass. } $$ There is no reference. Is that true ?
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2$\begingroup$ Yes, it is -- for a reference see e.g. the book by Grafakos, "Classical Fourier Analysis", subsection 2.5.4. $\endgroup$– Anton TselishchevCommented Jan 24 at 9:15
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$\begingroup$ Thanks. I unfortunately started my search by Grafakos "Modern Fourier Analysis". $\endgroup$– BazinCommented Jan 24 at 15:12
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