Characterisation by local means of mixed-norm Lizorkin-Triebel spaces

In the general theory of anisotropic mixed-nom Lizorkin-Triebel spaces, we have established a characterisation of the spaces in terms quasi-norms on temperate distributions.The norms involve convolutions and maximal functions of Peetre-Fefferman-Stein type. Local means in Triebel's terminology are covered as a special case. The main step consists in an extension of crucial inequalities due to Rychkov.
A manuscript has been worked out and submitted.