Sharp $L^p$-$L^q$ estimate for the spectral projection associated with the twisted Laplacian

In this note we are concerned with estimates for the spectral projection operator $\mathcal{P}_μ$ associated with the twisted Laplacian $L$. We completely characterize the optimal bounds on the operator norm of $\mathcal{P}_μ$ from $L^p$ to $L^q$ when $1\le p\le 2\le q\le \infty$. As an application, we obtain uniform resolvent estimate for $L$.

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