ON THE BOUUNDEDNESS OF FRACTIONAL B-MAXIMAL OPERATORS IN THE LORENTZ SPACES Lp,q,gamma >(R(+)n)

In this study, sharp rearrangement inequalities for the fractional B-maximal function M(alpha,gamma)f are obtained in the Lorentz spaces L-p,L-q,L-gamma and by using these inequalities the boundedness conditions of the operator M-alpha,M-gamma are found. Then, the conditions for the boundedness of the B-maximal operator M-gamma are obtained in L-p,L-q,L-gamma.