Integrability of maximal functions and Riesz potentials in Orlicz spaces of variable exponent

Our aim in this paper is to deal with Sobolevʹs type inequality, Hardyʹs type inequality and Trudingerʹs inequality for Riesz potentials of functions in Orlicz spaces of variable exponent. These results are based on the boundedness of maximal operators and so-called Hedbergʹs trick. Our methods can also be applied to the case of constant exponents with slight modifications.