Two-weight norm estimates for maximal and Calderón-Zygmund operators in variable exponent Lebesgue spaces (Q2854194)

The paper deals with two weight boundedness for maximal functions and singular integrals in variable exponent Lebesgue spaces defined on a space of homogeneous type (called SHT). Note that an important assumption in SHT is that the associated measure \(\mu\) is doubling, i.e. \(\mu (B(x, 2r)) \lesssim \mu (B(x,r))\). The main theorems in the paper give necessary and sufficient conditions such that the two-weight norm inequalities for some singular integrals in variable exponent Lebesgue spaces hold subject to some conditions on the weights. The difficult parts are to show the ``sufficiency part'', and the proofs are straightforward (in part it is on homogeneous space).