Hankel operators over complex manifolds

Hankel Operators over Complex Manifolds

Given a complex manifold M endowed with a hermitian metric g and supporting a smooth probability measure μ, there is a naturally associated Dirichlet form operator A on L(μ). If b is a function in L(μ) there is a naturally associated Hankel operator Hb defined in holomorphic function spaces over M . We establish a relation between hypercontractivity properties of the semigroup e−tA and boundedn...

Plemelj Projection Operators over Domain Manifolds

Plemelj projection operators are introduced for spaces of square integrable functions defined over the boundaries of a class of compact real n-dimensional manifolds lying in C. These manifolds posses many properties similar to domains in R, and are consequently called domain manifolds. The key ingredients used here are techniques from both real and complex Clifford analysis. Analogues of the Ke...

Hankel Operators in Several Complex Variables and Product Bmo

H(⊗1 C+) denotes the Hardy space of square integrable functions analytic in each variable separately. Let P be the natural projection of L(⊗1 C+) onto H (⊗1 C+). A Hankel operator with symbol b is the linear operator from H(⊗1 C+) to H (⊗1 C+) given by Hb φ = P⊖bφ. We show that ‖Hb‖ ≃ ‖P b‖BMO(⊗n 1 C+) , where the right hand norm is S.-Y. Chang and R. Fefferman product BMO. This fact has well k...

Distorted Hankel Integral Operators

For α, β > 0 and for a locally integrable function (or, more generally , a distribution) ϕ on (0, ∞), we study integral ooperators G α,β ϕ on L 2 (R +) defined by G α,β ϕ f (x) = R+ ϕ x α + y β f (y)dy. We describe the bounded and compact operators G α,β ϕ and operators G α,β ϕ of Schatten–von Neumann class S p. We also study continuity properties of the averaging projection Q α,β onto the oper...

Slant Hankel Operators