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On locally concave functions on simplest non-convex domains
Dmitriy Stolyarov, Pavel Zatitskiy
We prove that certain Bellman functions of several variables are the minimal locally concave functions. This generalizes earlier results about Bellman functions of two variables.
On Fourier multipliers with rapidly oscillating symbols
Dmitriy Stolyarov
We provide asymptotically sharp bounds for the norms of the Fourier multipliers with the symbols , where is a large parameter.
Fractional integration of summable functions: Maz'ya's -inequalities
Dmitriy Stolyarov
We study the inequalities of the type , where the kernel is homogeneous of order and possibly vector-v…
On -inequalities for martingale fractional integration and their Bellman functions
Dmitriy Stolyarov
Inspired by a conjecture of Vladimir Maz'ya on -inequalities in the spirit of Bourgain and Brezis, we establish some -inequalities for fractional martingale transforms. These…
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…