Characterization of Triebel-Lizorkin type spaces with variable exponents via maximal functions, local means and non-smooth atomic decompositions

In this paper we study the maximal function and local means characterizations and the non-smooth atomic decomposition of the Triebel-Lizorkin type spaces with variable exponents Fp(),q()s(),phi(Rn). These spaces were recently introduced by Yang etal. and cover the Triebel-Lizorkin spaces with variable exponents Fp(),q()s()(Rn) as well as the classical Triebel-Lizorkin spaces Fp,qs(Rn), even the case when p=. Moreover, covered by this scale are also the Triebel-Lizorkin-type spaces Fp,qs,(Rn) with constant exponents which, in turn cover the Triebel-Lizorkin-Morrey spaces. As an application we obtain a pointwise multiplier assertion for those spaces.