Local Characterizations of Besov and Triebel-Lizorkin Spaces with Variable Exponent

الملخص EN

We introduce new Besov and Triebel-Lizorkin spaces with variableintegrable exponent, which are different from those introduced by the second author early.

Then we characterize these spaces by the boundedness of the local Hardy-Littlewoodmaximal operator on variable exponent Lebesgue space.

Finally the completeness andthe lifting property of these spaces are also given.