## What is/are Singular Operators?

Singular Operators - Secondly, with the help of the Gunter derivatives, we reformulate the strongly-singular and hyper-singular integral operators into combinations of the weakly-singular operators and the tangential derivatives.^{[1]}At first, the matrix of the algebraic system is constructed as a 2 × 2 block matrix where the off-diagonal blocks consist of the Fourier coefficients of non-singular operators and the entries of the diagonal blocks involve the associated singularities.

^{[2]}In this paper, issues about the existence of a resolvent and separability (maximum smoothness of solutions) of a class of linear singular operators of the Korteweg-de Vries type in the case of an unbounded domain with strongly increasing coefficients are investigated.

^{[3]}The choice of the exponential basis functions of the form exp(−αr1−βr2−γr) allows us to construct an accurate and compact representation of the nonrelativistic wave function and to efficiently compute matrix elements of numerous singular operators representing relativistic and QED effects.

^{[4]}We introduce and study some operational quantities which characterize the disjointly non-singular operators from a Banach lattice E to a Banach space Y when E is order continuous, and some other quantities which characterize the disjointly strictly singular operators for arbitrary E.

^{[5]}Then we prove the boundedness of multilinear Calderón-Zygmund singular operators on weighted Lebesgue spaces and weighted Morrey-Herz spaces with variable exponents.

^{[6]}In the special case of the weakly and hypersingular operators on a line segment or screen, our approach gives a unified, independent proof for a series of recent results by Hiptmair, Jerez-Hanckes, Nedelec and Urzua-Torres.

^{[7]}We study the semigroups $$({\mathcal {C}}_p)_+$$(Cp)+, $$({\mathcal {C}}_p^{\text {dual}})_-$$(Cpdual)-, $${\mathcal {G}}_-$$G- and $${\mathcal {H}}_-$$H- associated with the operator ideals $${\mathcal {C}}_p$$Cp of p-converging operators ($$1

^{[8]}
In a variety of settings, we discuss two-sided norm estimates for commutators of classical singular operators with a symbol function.
^{[9]}
The results for singular operators will rely upon suitable convex body domination results, which in the case of commutators will be provided in this work, obtaining as a byproduct a new proof for the scalar case as well.
^{[10]}
In Conclusion, we discuss general methods of solution for problems with arbitrary singular operators.
^{[11]}
This is a survey on the existing answers up to the present day to the following questions: Is every lattice strictly singular operator also disjointly strictly singular? Do lattice strictly singular operators have a vector space structure?.
^{[12]}
We consider several weak type estimates for dyadic singular operators using the Bellman function approach.
^{[13]}
In the second part strictly singular and disjointly strictly singular operators between spaces $\lpv$ are studied.
^{[14]}
Recently, Lu and Zhu [16] established the boundedness of the multilinear Calderón-Zygmund singular operators on Morrey-Herz spaces with variable exponents.
^{[15]}

## Strictly Singular Operators

We introduce and study some operational quantities which characterize the disjointly non-singular operators from a Banach lattice E to a Banach space Y when E is order continuous, and some other quantities which characterize the disjointly strictly singular operators for arbitrary E.^{[1]}This is a survey on the existing answers up to the present day to the following questions: Is every lattice strictly singular operator also disjointly strictly singular? Do lattice strictly singular operators have a vector space structure?.

^{[2]}In the second part strictly singular and disjointly strictly singular operators between spaces $\lpv$ are studied.

^{[3]}

## Zygmund Singular Operators

Then we prove the boundedness of multilinear Calderón-Zygmund singular operators on weighted Lebesgue spaces and weighted Morrey-Herz spaces with variable exponents.^{[1]}Recently, Lu and Zhu [16] established the boundedness of the multilinear Calderón-Zygmund singular operators on Morrey-Herz spaces with variable exponents.

^{[2]}