Czechoslovak Mathematical Journal, first online, pp. 1-9
Notes on commutator on the variable exponent Lebesgue spaces
Received December 28, 2017. Published online March 22, 2019.
Abstract: We obtain the factorization theorem for Hardy space via the variable exponent Lebesgue spaces. As an application, it is proved that if the commutator of Coifman, Rochberg and Weiss $[b,T]$ is bounded on the variable exponent Lebesgue spaces, then $b$ is a bounded mean oscillation (BMO) function.
Keywords: bounded mean oscillation; commutator; Hardy space; variable exponent Lebesgue space