Singular integral operators, John–Nirenberg inequalities and Triebel–Lizorkin type spaces on weighted Lebesgue spaces with variable exponents

摘要

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