A Contraction of S U (2) to the Heisenberg Group.
Solvability of second-order left-invariant differential operators on the Heisenberg group
Su alcuni quozienti dell'algebra di Fourier centrale di un gruppo di Lie compatto
In this Note we give a proof for the particular case of the group of a local characterization of the central Fourier algebra of a compact Lie group in terms of the Fourier algebra of a maximal torus of . The proof for the general case will appear elsewhere [5]. We derive a result on local symbolic calculus for which partially extends a theorem of M. P. and P. Malliavin.
Norms of Harmonic Projection Operators on Compact Lie Groups.
Two-Parameter Maximal Functions in the Heisenberg Group.
Solvability for a class of non-homogeneous differential operators on two-step nilpotent groups.
Two-parameter maximal functions associated with homogeneous surfaces in
A unified approach to compact symmetric spaces of rank one
A relatively simple algebraic framework is given, in which all the compact symmetric spaces can be described and handled without distinguishing cases. We also give some applications and further results.
Spectral projections for the twisted Laplacian
Let n ≥ 1, d = 2n, and let (x,y) ∈ ℝⁿ × ℝⁿ be a generic point in ℝ²ⁿ. The twisted Laplacian has the spectrum n + 2k = λ²: k a nonnegative integer. Let be the spectral projection onto the (infinite-dimensional) eigenspace. We find the optimal exponent ϱ(p) in the estimate for all p ∈ [2,∞], improving previous partial results by Ratnakumar, Rawat and Thangavelu, and by Stempak and Zienkiewicz. The expression for ϱ(p) is ϱ(p) = 1/p -1/2 if 2 ≤ p ≤ 2(d+1)/(d-1), ϱ(p) = (d-2)/2 - d/p if 2(d+1)/(d-1)...
Boundary values of harmonic functions in mixed norm spaces and their atomic structure
Gelfand transforms of -invariant Schwartz functions on the free group
The spectrum of a Gelfand pair , where is a nilpotent group, can be embedded in a Euclidean space. We prove that in general, the Schwartz functions on the spectrum are the Gelfand transforms of Schwartz -invariant functions on . We also show the converse in the case of the Gelfand pair , where is the free two-step nilpotent Lie group with three generators. This extends recent results for the Heisenberg group.
Solvability of invariant sublaplacians on spheres and group contractions
In the first part of this paper we study the local and global solvability and the hypoellipticity of a family of left-invariant sublaplacians on the spheres . In the second part, we introduce a larger family of left-invariant sublaplacians on and study the corresponding properties by means of a Lie group contraction to the Heisenberg group.
Homogenous distributions on spaces of Hermitean matrices.
Bergman spaces on some tube-type domains and Laguerre operators on symmetric cones.
Two-parameter maximal functions associated with degenerate homogeneous surfaces in ℝ³
Multiparameter singular integrals and maximal functions
We prove -boundedness for a class of singular integral operators and maximal operators associated with a general -parameter family of dilations on . This class includes homogeneous operators defined by kernels supported on homogeneous manifolds. For singular integrals, only certain “minimal” cancellation is required of the kernels, depending on the given set of dilations.
Maximal functions and singular integrals associated to polynomial mapping of R.
Maximal functions and Hilbert transforms associated to polynomials.
Tangential Cauchy-Riemann equations on quadratic manifolds
We study the tangential Cauchy-Riemann equations for -forms on quadratic manifolds. We discuss solvability for data in the Schwartz class and describe the range of the tangential Cauchy-Riemann operator in terms of the signatures of the scalar components of the Levi form.
Fourier transform of Schwartz functions on the Heisenberg group
Let H₁ be the 3-dimensional Heisenberg group. We prove that a modified version of the spherical transform is an isomorphism between the space 𝓢ₘ(H₁) of Schwartz functions of type m and the space 𝓢(Σₘ) consisting of restrictions of Schwartz functions on ℝ² to a subset Σₘ of the Heisenberg fan with |m| of the half-lines removed. This result is then applied to study the case of general Schwartz functions on H₁.
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