In this paper, we prove Poincaré and Sobolev inequalities for differential forms in L^1(R^n). The singular integral estimates that it is possible to use for L^p, p > 1, are replaced here with inequalities whic...In this paper, we prove Poincaré and Sobolev inequalities for differential forms in L^1(R^n). The singular integral estimates that it is possible to use for L^p, p > 1, are replaced here with inequalities which go back to Bourgain and Brezis(2007).展开更多
This paper is divided in two parts： in Section 2, we define recursively a privileged basis of the primitive forms in a symplectic space（V^（2n）, ω）. Successively, in Section 3, we apply our construction in the se...This paper is divided in two parts： in Section 2, we define recursively a privileged basis of the primitive forms in a symplectic space（V^（2n）, ω）. Successively, in Section 3, we apply our construction in the setting of Heisenberg groups H^n, n ≥ 1, to write in coordinates the exterior differential of the so-called Rumin＇s complex of differential forms in H^n.展开更多
A Recursive Basis for Primitive Forms in Symplectic Spaces and Applications to Heisenberg Groups Annalisa BALDI Marilena BARNABEI Bruno FRANCHI Abstract This paper is divided in two parts:in Section 2,we define recurs...A Recursive Basis for Primitive Forms in Symplectic Spaces and Applications to Heisenberg Groups Annalisa BALDI Marilena BARNABEI Bruno FRANCHI Abstract This paper is divided in two parts:in Section 2,we define recursively a privileged basis of the primitive forms in a symplectic space(V^(2n),ω).Successively,in Section 3,we展开更多
基金supported by Funds for Selected Research Topics from the University of BolognaMAnET Marie Curie Initial Training Network+3 种基金GNAMPA (Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni) of INdAM (Istituto Nazionale di Alta Matematica "F. Severi"), ItalyPRIN (Progetti di Ricerca di Rilevante Interesse Nazionale) of the MIUR (Ministero dell’Istruzione dell’Università e della Ricerca), Italysupported by MAnET Marie Curie Initial Training Network, Agence Nationale de la Recherche (Grant Nos. ANR-10-BLAN 116-01 GGAA and ANR-15-CE40-0018 SRGI)the hospitality of Isaac Newton Institute, of EPSRC (Engineering and Physical Sciences Research Council) (Grant No. EP/K032208/1) and Simons Foundation
文摘In this paper, we prove Poincaré and Sobolev inequalities for differential forms in L^1(R^n). The singular integral estimates that it is possible to use for L^p, p > 1, are replaced here with inequalities which go back to Bourgain and Brezis(2007).
基金Supported by University of Bolognafunds for selected research topics+1 种基金supported by the Gruppo Nazionale per l’Analisi Matematica,la Probabilita e le loro Applicazioni(GNAMPA)of the Istituto Nazionale di Alta Matematica(INdA M)supported by P.R.I.N.of M.I.U.R.,Italy
文摘This paper is divided in two parts： in Section 2, we define recursively a privileged basis of the primitive forms in a symplectic space（V^（2n）, ω）. Successively, in Section 3, we apply our construction in the setting of Heisenberg groups H^n, n ≥ 1, to write in coordinates the exterior differential of the so-called Rumin＇s complex of differential forms in H^n.
文摘A Recursive Basis for Primitive Forms in Symplectic Spaces and Applications to Heisenberg Groups Annalisa BALDI Marilena BARNABEI Bruno FRANCHI Abstract This paper is divided in two parts:in Section 2,we define recursively a privileged basis of the primitive forms in a symplectic space(V^(2n),ω).Successively,in Section 3,we
