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math.CA2018
Fractional smoothness in with Dunkl weight and its applications
D. V. Gorbachev, V. I. Ivanov
We define fractional power of the Dunkl Laplacian, fractional modulus of smoothness and fractional -functional in -space with the Dunkl weight. As application, we prove dir…
math.AP2018
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…