Local Characterizations of Besov and Triebel-Lizorkin Spaces with Variable Exponent - Baohua Dong; Jingshi Xu (Journal of Function Spaces)
We introduce new Besov and Triebel-Lizorkin spaces with variable integrable exponent, which are different from those introduced by the second author early. Then we characterize these spaces by the boundedness of the local Hardy-Littlewood maximal operator on variable exponent Lebesgue space. Finally the completeness and the lifting property of these spaces are also given.