Weighted gradient inequalities and unique continuation problems

laura De Carli, Dmitry Gorbachev, Sergey Tikhonov

We use Pitt inequalities for the Fourier transform to prove the following weighted gradient inequality $$ \|e^{-τ\ell(\cdot)} u^{\frac 1q} f\|_q\leq c_τ\| e^{-τ\ell(\cdot)} v^{\fra…