Boundedness of some bilinear operators on variable Herz-type Hardy spaces

This paper is concerned with proving some estimate on variable Herz-type Hardy spaces of bilinear operators B(f, g)(x) = Sigma(N)(gamma=1) (T-gamma(1) f) (x) (T-gamma(2) g) (x), x is an element of R-n, where N is an element of N, T-gamma(1) and T-gamma(2) are operators satisfying certain conditions. More precisely we prove the boundedness of B from H(K) over dot(p1(.))(alpha 1(.), q1(.)) (R-n) x (K) over dot(p2(.))(alpha 2(.), q2(.)) (R-n) into H(K) over dot(p(.))(alpha(.), q(.)) (R-n) and from H(K) over dot(p1(.))(alpha 1(.), q1(.)) (R-n) x H(K) over dot(p2(.))(alpha 2(.), q2(.)) (R-n) into H(K) over dot(p(.))(alpha(.), q(.)) (R-n), with some appropriate assumptions on the parameters alpha(.), alpha(i)(.), p(.), p(i)(.), q(.) and q(i)(.), i = 1, 2. Our results cover the results on Herz-type Hardy spaces with fixed exponents.