870 research outputs found
Bilinear Riesz means on the Heisenberg group
In this article, we investigate the bilinear Riesz means
associated to the sublaplacian on the Heisenberg group. We prove that the
operator is bounded from into for and when is large than a suitable smoothness index .
There are some essential differences between the Euclidean space and the
Heisenberg group for studying the bilinear Riesz means problem. We make use of
some special techniques to obtain a lower index
Wiener measure for Heisenberg group
In this paper, we build Wiener measure for the path space on the Heisenberg
group by using of the heat kernel corresponding to the sub-Laplacian and give
the definition of the Wiener integral. Then we give the Feynman-Kac formula.Comment: 14 page
The intrinsic square function characterizations of weighted Hardy spaces
In this paper, we will study the boundedness of intrinsic square functions on
the weighted Hardy spaces for , where is a Muckenhoupt's
weight function. We will also give some intrinsic square function
characterizations of weighted Hardy spaces for .Comment: 17 page
A functional calculus and restriction theorem on H-type groups
Let be the sublaplacian and the partial Laplacian with respect to
central variables on H-type groups. We investigate a class of invariant
differential operators by the joint functional calculus of and . We
establish Stein-Tomas type restriction theorems for these operators. In
particular, the asymptotic behaviors of restriction estimates are given
Boundedness of the bilinear Bochner-Riesz Means in the non-Banach triangle case
In this article, we investigate the boundedness of the bilinear Bochner-Riesz
means in the non-Banach triangle case. We improve the
corresponding results in [Bern] in two aspects: Our partition of the non-Banach
triangle is simpler and we obtain lower smoothness indices for various cases apart from
Permanental polynomials of skew adjacency matrices of oriented graphs
Let be an orientation of a simple graph . In this paper, the
permanental polynomial of an oriented graph is introduced. The
coefficients of the permanental polynomial of are interpreted in
terms of the graph structure of , and it is proved that all
orientations of have the same permanental polynomial if and only
if has no even cycles. Furthermore, the roots of the permanental polynomial
of are studied.Comment: 1 figur
Hardy spaces associated with Schrodinger operators on the Heisenberg group
Let be a Schr\"odinger operator on the
Heisenberg group , where is the
sub-Laplacian and the nonnegative potential belongs to the reverse H\"older
class and is the homogeneous dimension of .
The Riesz transforms associated with the Schr\"odinger operator are bounded
from to . The
integrability of the Riesz transforms associated with characterizes a
certain Hardy type space denoted by which is larger than
the usual Hardy space . We define in
terms of the maximal function with respect to the semigroup , and give the atomic decomposition of . As an
application of the atomic decomposition theorem, we prove that
can be characterized by the Riesz transforms associated
with . All results hold for stratified groups as well.Comment: 42 page
Sharp Hardy-Littlewood-Sobolev Inequalities on Octonionic Heisenberg Group
This paper is a second one following our work [CLZ13] in series, considering
sharp Hardy- Littlewood-Sobolev inequalities on groups of Heisenberg type. The
first important breakthrough was made by Frank and Lieb in [FL12]. In this
paper, analogous results are obtained for octonionic Heisenberg group.Comment: 14 page
Remainder Terms for Several Inequalities on Some Groups of Heisenberg-type
We give some estimates of the remainder terms for several
conformally-invariant Sobolev-type inequalities on the Heisenberg group, in
analogy with the Euclidean case. By considering the variation of associated
functionals, we give a stability of two dual forms: the fractional Sobolev
(Folland-Stein) and Hardy-Littlewood-Sobolev inequality, in terms of distance
to the submanifold of extremizers. Then we compare their remainder terms to
improve the inequalities in another way. We also compare, in the limit case s =
Q (or = 0), the remainder terms of Beckner-Onofri inequality and its
dual Logarithmic Hardy-Littlewood-Sobolev inequality. Besides, we also list
without proof some results for the other two cases of groups of Iwasawa-type.
Our results generalize earlier works on Euclidean spaces by Chen, Frank, Weth
[CFW13] and Dolbeault, Jankowiakin [DJ14] onto some groups of Heisenberg-type.Comment: 18 page
Surface-Plasmon-Polariton (SPP)-Like Acoustic Surface Waves on Elastic Metamaterials
We investigate the dispersion properties of the acoustic surface waves on
surface of elastic metamaterials. With an analytical approach, we show that
unconventional acoustic surface waves, with dispersion behaviors very similar
to the electromagnetic surface plasmon polaritons (SPPs) on metal surfaces, can
exist on the elastic metamaterials around the frequency at which the elastic
Lam\'e's constants satisfy lambda+mu=0. Two typical elastic metamaterials are
exemplified to demonstrate such peculiar acoustic surface waves.Comment: 14 pages, 4 figure
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