Characterisation by Local Means of Anisotropic Lizorkin--Triebel Spaces   with Mixed Norms
  This is a contribution to the theory of Lizorkin--Triebel spaces having mixed Lebesgue norms and quasi-homogeneous smoothness. We discuss their characterisation in terms of general quasi-norms based on convolutions. In particular, this covers the case of local means, in Triebel's terminology. The main step is an extension of some crucial inequalities due to Rychkov to the case with mixed norms. 
Jon Johnsen, Sabrina Munch Hansen, Winfried Sickel
math.FA