Defect Distributions Related to Weakly Convergent Sequences in Bessel-Type Spaces $${H_{\Lambda }^{-s,p}}$$

We consider microlocal defect distributions associated to a weakly convergent sequences \(u_n\) in \(H^{-s,p}_{\Lambda }\) and \(v_n\) in \(H^{s+m,q}_{\Lambda }\) through the space of pseudo-differential operators with the symbols in \((s^{m,N+1}_\Lambda )_0\). Symbols correspond to a weight function \(\Lambda \) determining a quasi-elliptic symbol. Results are applied to partial differential equations with symbols related to weights of the type \(\Lambda \).