Change of variable results for 𝐴_{𝑝}- and reverse Hölder 𝑅𝐻ᵣ-classes

Abstract

We study conditions under which the map \[ T h , γ w ( x ) = w ( h ( x ) ) | h ′ ( x ) | γ {T_{h,\gamma }}w(x)= w(h(x))|h’(x){|^\gamma } \] maps the Muckenhoupt class A p {A_p} into A q {A_q} and the reverse Hölder class R H r 1 R{H_{{r_1}}} into R H r 2 R{H_{{r_2}}} .