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

Kwok Pun Ho

• 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.