On weighted Lizorkin-Triebel spaces. Singular integrals, multipliers, imbedding theorems
The author considers the Lizorkin-Triebel type spaces \(L^{p,\theta}_{\omega,m}\) with a Muckenhoupt type weight function \(\omega\). He gives the theorems on Fourier multipliers for \(L^{p,\theta}_{\omega,m}\)-spaces. By means of the method of multipliers he develops the complete imbedding theory for \(L^{p,\theta}_{\omega,m}\)-spaces in the case of different metrics and of different dimensions. The author gives also the theorem on the boundedness of the maximal singular operator generated by an n-tuple singular operator in the space \(L^ p_{\omega}\). The exact characterization of weight functions \(\omega\) is given for an n-tuple singular integral operator to be bounded in the space \(L^ p_{\omega}\).
scientific article; zbMATH DE number 3921263