11 papers
Dimension estimates for vectorial measures with restricted spectrum
Dmitriy Stolyarov
We link the problem of estimating the lower Hausdorff dimension of PDE or Fourier constrained measures with Harnack's inequalities for the heat equation. Our approach provides new…
Hardy--Littlewood--Sobolev inequality for
Dmitriy Stolyarov
Let be a closed dilation and translation invariant subspace of the space of -valued Schwartz distributions in variables. We show that if the spac…
Fractional integration for irregular martingales
Dmitriy Stolyarov, Dmitry Yarcev
We suggest two versions of the Hardy--Littlewood--Sobolev inequality for discrete time martingales. In one version, the fractional integration operator is a martingale transform, h…
Weakly canceling operators and singular integrals
Dmitriy Stolyarov
We suggest an elementary Harmonic Analysis approach to canceling and weakly canceling differential operators, which allows to extend these notions to anisotropic setting and also r…
Hausdorff dimension of measures with arithmetically restricted spectrum
Rami Ayoush, Dmitriy Stolyarov, Michał Wojciechowski
We provide an estimate from below for the lower Hausdorff dimension of measures on the unit circle based on the arithmetic properties of their spectra. We obtain our bounds via app…
Sharp mutliplicative inequalities with
Dmitriy Stolyarov, Vasily Vasyunin, Pavel Zatitskiy
We find the best possible constant in the inequality , where and . We employ t…