Boundedness of metaplectic operators within $L^p$ spaces, applications to pseudodifferential calculus, and time-frequency representations

Gianluca Giacchi

Housdorff-Young's inequality establishes the boundedness of the Fourier transform from $L^p$ to $L^q$ spaces for $1\le p\le 2$ and $q=p^{\prime }$, where $p^{\prime }$ denotes the Lebesgue-conjugat…