Generalized absolute Hausdorff summability of orthogonal series

For 1a parts per thousand broken vertical bar ka parts per thousand broken vertical bar 2 and a sequence that is quasi beta-power monotone decreasing with , we prove the |A,gamma| (k) summability of an orthogonal series, where A is either a regular or Hausdorff matrix. For , we give a necessary and sufficient condition for |A,gamma| (k) summability, where A is Hausdorff matrix. Our sufficient condition for is weaker than that of Kantawala [1], for |E,q,gamma| (k) summability; and of Leindler [4], beta >-1 for |C,alpha,gamma| (k) , . Also, our result generalizes the result of Spevakov [6] for |E,q,1|(1) summability.