An alternative to Plancherel’s criterion for bilinear operators
Volume 119 / 2019
Banach Center Publications 119 (2019), 173-179
MSC: 42B15, 42B20, 42B99.
DOI: 10.4064/bc119-9
Abstract
We prove that bilinear operators associated with $L^q$ multipliers with sufficiently many derivatives in $L^\infty $ are bounded from $L^2\times L^2$ to $L^1$ when $q \lt 4$. In the absence of Plancherel’s identity on $L^1$, the range $q \lt 4$ in the bilinear case should be compared to $q=\infty $ in the classical $L^2\to L^2$ boundedness for linear multiplier operators.
