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The aim of this paper is to establish the relation between the two classes of functionsBV  *   ⁢   (  q  ;  α  ){\mathrm{BV}_{*}(q;\alpha)}    andΛ  *   ⁢   BV  p{\Lambda_{*}\mathrm{BV}^{p}}   . It uses a new shorter proof and extends the results of Gogatishvili, Goginava and Tephnadze.

Relations between BV * ( q ;α) and Λ * BV p classes of functions