The Riesz transforms associated with second order differential operators

1989 ◽  
pp. 1-43 ◽  
Author(s):  
Dominique Bakry
Keyword(s):  
Differential Operators ◽  
Second Order ◽  
Riesz Transforms

Factorization of Linear Second Order Differential Operators

1964 ◽  
Vol 37 (5) ◽  
pp. 302-304
Author(s):  
J. H. Heinbockel
Keyword(s):  
Differential Operators ◽  
Second Order

scholarly journals AdS superprojectors

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
E. I. Buchbinder ◽  
D. Hutchings ◽  
S. M. Kuzenko ◽  
M. Ponds
Keyword(s):  
Shell Model ◽  
Differential Operators ◽  
Second Order ◽  
Projection Operators ◽  
De Sitter ◽  
Gauge Invariant ◽  
Gauge Transformations ◽  
Four Dimensions ◽  
Higher Spin

Abstract Within the framework of $$ \mathcal{N} $$ N = 1 anti-de Sitter (AdS) supersymmetry in four dimensions, we derive superspin projection operators (or superprojectors). For a tensor superfield $$ {\mathfrak{V}}_{\alpha (m)\overset{\cdot }{\alpha }(n)}:= {\mathfrak{V}}_{\left(\alpha 1\dots \alpha m\right)\left({\overset{\cdot }{\alpha}}_1\dots {\overset{\cdot }{\alpha}}_n\right)} $$ V α m α ⋅ n ≔ V α 1 … αm α ⋅ 1 … α ⋅ n on AdS superspace, with m and n non-negative integers, the corresponding superprojector turns $$ {\mathfrak{V}}_{\alpha (m)\overset{\cdot }{\alpha }(n)} $$ V α m α ⋅ n into a multiplet with the properties of a conserved conformal supercurrent. It is demonstrated that the poles of such superprojectors correspond to (partially) massless multiplets, and the associated gauge transformations are derived. We give a systematic discussion of how to realise the unitary and the partially massless representations of the $$ \mathcal{N} $$ N = 1 AdS4 superalgebra $$ \mathfrak{osp} $$ osp (1|4) in terms of on-shell superfields. As an example, we present an off-shell model for the massive gravitino multiplet in AdS4. We also prove that the gauge-invariant actions for superconformal higher-spin multiplets factorise into products of minimal second-order differential operators.

Second-order Riesz Transforms and Maximal Inequalities Associated with Magnetic Schr ödinger Operators

2015 ◽  
Vol 58 (2) ◽  
pp. 432-448 ◽  
Author(s):  
Dachun Yang ◽  
Sibei Yang
Keyword(s):  
Hardy Space ◽  
Orlicz Space ◽  
Orlicz Function ◽  
Second Order ◽  
Riesz Transforms ◽  
Muckenhoupt Weights ◽  
Schrodinger Operator ◽  
Magnetic Schrödinger Operator ◽  
Maximal Inequalities ◽  
Reverse Hölder

AbstractLet be a magnetic Schrödinger operator on ℝn, wheresatisfy some reverse Hölder conditions. Let be such that ϕ(x, ·) for any given x ∊ ℝn is an Orlicz function, ϕ( ·, t) ∊ A∞(ℝn) for all t ∊ (0,∞) (the class of uniformly Muckenhoupt weights) and its uniformly critical upper type index . In this article, the authors prove that second-order Riesz transforms VA-1 and are bounded from the Musielak–Orlicz–Hardy space Hµ,A(Rn), associated with A, to theMusielak–Orlicz space Lµ(Rn). Moreover, we establish the boundedness of VA-1 on . As applications, some maximal inequalities associated with A in the scale of Hµ,A(Rn) are obtained

Sign in / Sign up

Export Citation Format

Share Document