Asymptotic behavior of the weighted cross-variation with respect to fractional Brownian sheet

By using the techniques of Malliavin calculus, we investigate the asymptotic behavior of the weighted cross-variation of fractional Brownian sheet with the case when Hurst parameter H=(H1,H2)H=(H1,H2) belongs to (0,1/2)×(1/2,1)(0,1/2)×(1/2,1) or (1/2,1)×(0,1/2)(1/2,1)×(0,1/2).