New inequalities for weaving frames in Hilbert spaces

In this paper, we establish Parseval identities and surprising new inequalities for weaving frames in Hilbert space, which involve scalar $\lambda \in \text{rs}$. By suitable choices of $\lambda$, one obtains the previous results as special cases. Our results generalize and improve the remarkable results which have been obtained by Balan et al. and G\u{a}vru\c{t}a.