arXiv subjects

A. Bonami

Publications and source records attributed to A. Bonami.

3 recordsLinked to original sources

arXiv2009

Analytic Besov spaces and Hardy-type inequalities in tube domains over symmetric cones

We give various equivalent formulations to the (partially) open problem about $L^p$-boundedness of Bergman projections in tubes over cones. Namely, we show that such boundedness is equivalent to the duality identity between Bergman spaces, $A^{p'}=(A^p)^*$, and also to a Hardy type inequality related to the wave operator. We introduce analytic Besov spaces in tubes over cones, for which such Hardy inequalities play an important role. For $p\geq 2$ we identify as a Besov space the range of the Bergman projection acting on $L^p$, and also the dual of $A^{p'}$. For the Bloch space $\SB^\infty$ we give in addition new necessary conditions on the number of derivatives required in its definition.

math.CA↗

arXiv2003

Littlewood-Paley decompositions and Besov spaces related to symmetric cones

Starting from a Whitney decomposition of a symmetric cone $Ω$, analog to the dyadic partition $[2^j, 2^{j+1})$ of the positive real line, in this paper we develop an adapted Littlewood-Paley theory for functions with spectrum in $Ω$. In particular, we define a natural class of Besov spaces of such functions, $B^{p,q}_ν$, where the role of usual derivation is now played by the generalized wave operator of the cone $Δ(\frac{\partial}{\partial x})$. Our main result shows that $B^{p,q}_ν$ consists precisely of the distributional boundary values of holomorphic functions in the Bergman space $A^{p,q}_ν(T_Ω)$, at least in a ``good range'' of indices $1\leq q 2$. Moreover, we show the equivalence of this problem with the boundedness of Bergman projectors $P_ν\colon L^{p,q}_ν\to A^{p,q}_ν$, for which our result implies a positive answer when $q_{ν,p}'<q<q_{ν,p}$. This extends to general cones previous work of the authors in the light-cone. Finally, we conclude the paper with a finer analysis in light-cones, for which we establish a link between our conjecture and the cone multiplier problem. Moreover, using recent work by Tao, Vargas and Wolff, we improve in dimension 3 the range of $q$'s for which the Bergman projection is bounded.

math.CA↗

arXiv2000

Hua system and pluriharmonicity for symmetric irreducible Siegel domains of type II

We consider the Johnson-Koranyi-Hua system on symmetric Siegel domains of type two. We prove that all functions which are annihilated by the system and satisfy an H^2 integrability condition are pluriharmonic. So the situation is completely different on type two domains than on tube type domains: it was proved by Johnson and Koranyi that on symmetric tube type domains the system characterizes Poisson-Szego integrals.

math.CV↗