Elementary aspects ofB p,q s (Kn) andF p,q s (Kn) spaces

In the first part of this paper, we discuss some properties of S^Ω(K_n), L _P ^Ω (K_n) and L _P ^Ω (K_n;l_q) spaces, give the Plancherel-Polya-Nikol’skij type inequalities and some multiplier theorems. In the second part of this paper, using the results of Part I we prove some preliminary results for the spaces B _p,q ^s (K_n) and F _p,q ^s (K_n).