Sulfonamide derivatives having a matrix metalloprotease inhibiting effect, which are compounds represented by general formula (I), optical isomers of the same, pharmaceutically acceptable salts of both, or solvates of them: wherein R1 and R2 are each independently hydrogen atom, optionally substituted lower alkyl or the like; R3 is optionally substituted aryl, optionally substituted heteroaryl or the like; X is —CH═CH—, —O—, or —S—; Y is NHOH, hydroxy, or lower alkyloxy.