255 research outputs found
Spectral Multipliers on 2-Step Stratified Groups, II
No full textGiven a graded group G and commuting, formally self-adjoint, left-invariant, homogeneous differential operators L_1,..., L_n on G, one of which is Rockland, we study the convolution operators m(L_1,..., L_n) and their convolution kernels, with particular reference to the case in which G is abelian and n=1, and the case in which G is a 2-step stratified group which satisfies a slight strengthening of the Moore-Wolf condition and L_1,..., L_n are either sub-Laplacians or central elements of the Lie algebra of G.
Under suitable conditions, we prove that: i) if the convolution kernel of the operator m(L_1,..., L_n) belongs to L^1, then m equals almost everywhere a continuous function vanishing at infinity (`Riemann-Lebesgue lemma'); ii) if the convolution kernel of the operator m(L_1,..., L_n) is a Schwartz function, then m equals almost everywhere a Schwartz function
Paley–Wiener–Schwartz theorems on quadratic CR manifolds
No full textGiven a quadratic CR manifold M embedded in a complex space, we study Paley–Wiener–Schwartz theorems for spaces of Schwartz functions and tempered distributions on M. We discuss the interpretation of the space of restrictions of entire functions of exponential growth to M in terms of their non-commutative Fourier transform. We provide some structure results of the considered entire functions of exponential growth in terms of the geometric properties of M
Weighted sub-Laplacians on M\'etivier Groups: Essential Self-Adjointness and Spectrum
No full textLet be a M\'etivier group and let be any homogeneous norm on . For
denote by the function and consider the
weighted sub-Laplacian associated with the Dirichlet
form ,
where is the horizontal gradient on . Consider
with domain . We prove that
is essentially self-adjoint when . For
a particular , which is the norm appearing in 's fundamental
solution when is an H-type group, we prove that
has purely discrete spectrum if and only if , thus proving a
conjecture of J. Inglis.Comment: 15 pages; to appear on Proc. Amer. Math. So
A Note on Hardy Spaces on Quadratic CR Manifolds
No full textGiven a quadratic CR manifold M embedded in a complex space, and a holomorphic function f on a tubular neighbourhood of M, we show that the Lp-norms of the restrictions of f to the translates of M is decreasing for the ordering induced by the closed convex envelope of the image of the Levi form of M
Functional Calculus on Homogeneous Groups
No full textDati degli operatori differenziali congiuntamente ipoellittici, formalmente autoaggiunti, omogenei ed invarianti a sinistra L_1,..., L_n su un gruppo stratificato G, si considera la trasformata nucleo K ad essi associata. Vengono presentati su gruppi di Heisenberg degli esempi relativi allo studio delle proprietà: (RL) se K(m) è integrabile, allora m è continua; (S) se K(m) è di Schwartz, allora m è di Schwartz
Besov Spaces of Analytic Type: Interpolation, Convolution, Fourier Multipliers, Inclusions
No full textWe consider a family of Besov spaces of analytic type on the Shilov boundary
of a homogeneous Siegel domain , and study their properties in
relation to convolution, Fourier multipliers, and complex interpolation. In
addition, we study how these Besov spaces of analytic type can be compared with
the `classical' Besov spaces .Comment: 38 pages, no figure
Moltiplicatori spettrali su gruppi omogenei
No full textPresi degli operatori differenziali omogenei, formalmente autoaggiunti, congiuntamente ipoellittici ed invarianti a sinistra L_1,..., L_n su un gruppo omogeneo G, si considera la trasformata nucleo K ad essi associata. Si studiano, nel contesto dei gruppi abeliani e dei gruppi di Heisenberg, le proprietà: (RL) se K(m) è integrabile, allora m è continua; (S) se K(m) è di Schwartz, allora m è di Schwartz
Spectral Multipliers on Stratified Groups
No full textGiven jointly hypoelliptic, formally self-adjoint, homogeneous, left-invariant differential operators L_1,..., L_n on a stratified group G, the associated kernel transform K is studied. In particular, the following properties are investigated: (RL) if K(m) is integrable, then m is continuous; (S) if K(m) is Schwartz, then m is Schwartz
Boundedness of Bergman projectors on homogeneous Siegel domains
No full textIn this paper we study the boundedness of Bergman projectors on weighted
Bergman spaces on homogeneous Siegel domains of Type II. As it appeared to be a
natural approach in the special case of tube domains over irreducible symmetric
cones, we study such boundedness on the scale of mixed-norm weighted Lebesgue
spaces.
The sharp range for the boundedness of such operators is essentially known
only in the case of tube domains over Lorentz cones.
In this paper we prove that the boundedness of such Bergman projectors is
equivalent to variuos notions of atomic decomposition, duality, and
characterization of boundary values of the mixed-norm weighted Bergman spaces,
extending results moslty known only in the case of tube domains over
irreducible symmetric cones. Some of our results are new even in the latter
simpler context.
We also study the simpler, but still quite interesting, case of the
"positive" Bergman projectors, the integral operator in which the Bergman
kernel is replaced by its absolute value. We provide a useful characterization
which was previously known for tube domains.Comment: 34 pages, no figure
Carleson and Reverse Carleson Measures on Homogeneous Siegel Domains
No full textIn this paper we study Carleson and reverse Carleson measures for holomorphic function spaces on a homogeneous Siegel domain of Type II. We prove several necessary conditions and sufficient conditions in order for a measure μ to be Carleson and reverse Carleson on mixed-normed weighted Bergman spaces
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