Real interpolation identity for mixed Lorentz spaces

Establish or refute the real interpolation identity \((L^{q_0,\infty}L^{p_0},L^{q_1,\infty}L^{p_1})_{\theta,q}=L^qL^{p,q}\) under the stated exponent and interpolation conditions.

Background

A cited argument claimed the critical orthonormal Strichartz estimate on the entire region $(OCDA)^o$ by combining an existing estimate with a real interpolation formula for mixed Lorentz spaces. The paper points out that the validity of this interpolation identity is itself unresolved.

Consequently, the cited argument cannot presently be used to establish the claimed estimates throughout that region. The open issue concerns the interpolation identity directly, not merely its application to orthonormal Strichartz estimates.