The phrase "associated to a singular" is not correct in standard written English.
The correct preposition to use in this context is "with" instead of "to."
Example: "The data is associated with a singular event in the study."
Alternatives: "linked to a singular" or "related to a singular."
We consider the spectral behavior of the Laplace Beltrami operator associated to a class of singular perturbations of a Riemannian metric on a complete manifold.
We consider singular integrals associated to a classical Calderón Zygmund kernel K and a hypersurface given by the graph of ϕ(ψ(t)) where ϕ is an arbitrary C1 function and ψ is a smooth convex function of finite type.
In this paper, we prove the M 2 -type sharp maximal function estimates for the Toeplitz-type operators associated to certain singular integral operators satisfying a variant of Hörmander's condition.
To this end, we must remove the contribution of the singular vectors associated to the largest singular value d 1 using: boldsymbol{K}_{xy} - d_{1}boldsymbol{u}_{1}boldsymbol{v}_{1}^{T} = sumlimits_{i=2}^{N}d_{i}boldsymbol{u}_{i}boldsymbol{v}_{i}^{T}~.
Therefore, we can observe that X T w x and Y T w y are the left singular vectors associated to the largest singular values of the matrices K xy =P x P y and K yx =P y P x respectively.
In [13], the boundedness of the commutator associated to the singular integral operator with non-smooth kernel is obtained.
In this paper, we study some multilinear operator associated to the singular integral operators with non-smooth kernels as follows.
In [12 16], the boundedness of the commutator associated to the singular integral operator with non-smooth kernel are obtained.
In [6 8], some Toeplitz-type operators associated to the singular integral operators and strongly singular integral operators were introduced, and the boundedness for the operators was obtained.
