Szego Kernel Asymptotics for High Power of CR Line Bundles and Kodaira Embedding Theorems on CR Manifolds

Let $X$ be an abstract not necessarily compact orientable CR manifold of dimension $2n-1$, $ngeqslant 2$, and let $L^k$ be the $k$-th tensor power of a CR complex line bundle $L$ over $X$. Given $qin {0,1,ldots,n-1}$, let $Box ^{(q)}_{b,k}$ be the Gaffney extension of Kohn Laplacian for $(0,q)$ forms with values in $L^k$.