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I will discuss the Hardy-Littlewood integral inequality with sharp constant on the Heisenberg goup proved by Frank and Lieb. I will outline a simpler proof which bypasses the sophisticated argument fo...
Since the work by Caffarelli-Chan-Silvestre-Vasseur, integro-differential equations naturally arise from models in physics, engineering, and finance, attracting an increasing level of interest. They a...
Since the work by Caffarelli-Chan-Silvestre-Vasseur, integro-differential equations naturally arise from models in physics, engineering, and finance, attracting an increasing level of interest. They a...
We de ne higher categorical invariants (gerbes) of codimension two algebraic cycles and provide a categorical interpretation of the intersection of divisors on a smooth proper algebraic variety. This...
It is a folk conjecture that for alpha > 1/2 there is no alpha-Hoelder surface in the subRiemannian Heisenberg group. Namely, it is expected that there is no embedding from an open subset of R^2 into ...
Gabor frames with Hermite functions are equivalent to sampling sequences in true Fock spaces of polyanalytic functions. In the L2-case, such an equivalence follows from the unitarity of the polyanalyt...
In this paper we provide a characterization of second order fully nonlinear CR invariant equations on the Heisenberg group, which is the analogue in the CR setting of the result proved in the Euclide...
We determine the best (optimal) constant in the L2 Folland-Stein inequality on the quaternionic Heisenberg group and the non-negative functions for which equality holds.
We derive the sharp constants for the inequalities on the Heisenberg group Hn whose analogues on Euclidean space Rn are the well known Hardy-Littlewood- Sobolev inequalities. Only one special case had...
In the first Heisenberg group, we show that the intersection of two intrinsic submanifolds with linearly independent horizontal normals locally coincides with the image of an injective continuous curv...
In this paper some Poincare type inequalities are obtained for the maps of the Heisenberg group target.
Some Hardy type inequalities on the domain in the Heisenberg group are established by using the Picone type identity and constructing suitable auxiliary functions.
Let $f$ be in the localized nonisotropic Sobolev space $W_{\rm loc}^{1,p}(\Bbb H^n) $ on the $n$-dimensional Heisenberg group $\Bbb H^n=\Bbb C^n\times \Bbb R$, where $1\leq p is the h...
Let G=H2n+1 be a (2n+1)-dimensional Heisenberg Lie group acts on M=Cm-\{0\} and M'=Cm'-\{0\} exponentially. By using Cohomological Index we proved the following theorem. If f:M{\to}M' is a G-equivaria...

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