Singular integral operators, john–nirenberg inequalities and triebel–lizorkin type spaces on weighted lebesgue spaces with variable exponents

We establish the boundedness of singular integral operators, the Fefferman–Stein inequality and the John–Nirenberg inequalities on weighted Lebesgue spaces with variable exponents by using the extrapolation theorem. Moreover, as a consequence of the extrapolation theorem, we have the Fefferman–Stein vector-valued inequalities on weighted Lebesgue spaces, and hence we use it to study the weighted Triebel–Lizorkin spaces with variable exponent. Copyright © 2016 Unión Matemática Argentina.