B-maximal operators, B-singular integral operators and B-Riesz potentials in variable exponent Lorentz spaces

Abstract

In this paper, we prove the boundedness of B-maximal operator, B-singular integral operator and B-Riesz potential in the variable exponent Lorentz space Lp(center dot),q(center dot),gamma(Rnk,+). As a consequence of the boundedness of B-Riesz potentials in variable exponent Lorentz spaces, we also obtain that B-fractional maximal operators are bounded in Lp(center dot),q(center dot),gamma(Rnk,+).